Practice: perimeter and area

Geometry, grade 7 Lesson 14 of 18Practice

Practice: perimeter and area

1

Calculate the area.

a

a rectangle, 12 cm by 7.5 cm

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

a square with a side of 1.5 m

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

c

a parallelogram: a side of 9 cm, the height to it 6 cm

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

d

a triangle: a side of 14 cm, the height to it 5 cm

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

e

a trapezoid: bases 11 cm and 7 cm, height 4 cm

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

f

a right triangle; the legs: 3 m and 4.2 m

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

2

The perimeter of a rectangle is 34 cm.
One of its sides is 12 cm.
Find the other side and the area of the rectangle.

a

the other side, in cm

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

the area, in cm²

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

3

A square and a rectangle have the same perimeter, 40 cm.
One of the rectangle’s sides is 14 cm.
Which of the two shapes has the larger area, and by how much?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

4

$\displaystyle ABCD$ is a parallelogram, and $\displaystyle DE$ is the height to the side $\displaystyle AB$ .
The lengths are in cm.
Find the area of the parallelogram and the height to the side $\displaystyle AD$ .

a

the area, in cm²

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

the height to the side

\displaystyle AD

, in cm

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

5

$\displaystyle ABCD$ is a parallelogram, and the point $\displaystyle E$ is on the side $\displaystyle DC$ .
$\displaystyle DH$ is the height to the side $\displaystyle AB$ .
The lengths are in cm.
Calculate the area of the parallelogram and the area of the triangle $\displaystyle ABE$ .

a

the parallelogram, in cm²

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

the triangle

\displaystyle ABE

, in cm²

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

6

Each square is one unit of area.
Calculate the area of the triangle $\displaystyle ABC$ .

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

7

This is the plan of the living room in Maya’s home. The lengths in the drawing are in metres.
Find the area of the floor and its perimeter.
The floor is covered with parquet, which costs 120 ₪ per m². How much will the parquet for the whole floor cost?

a

the area, in m²

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

the perimeter, in m

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

c

the price, in ₪

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

8

A wall 5 m wide and 2.8 m high is to be painted.
The wall has a window 1.5 m by 1.2 m, which is not painted.
A tin of paint is enough for 6 m².
How many tins of paint must be bought? Explain.

9

A kitchen floor is a rectangle 3.6 m by 2.4 m.
It is tiled with square tiles, 30 cm by 30 cm.
How many tiles are needed?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

10

A bed in a garden is a trapezoid.
Its bases are 6 m and 4 m, and its height is 3 m.
4 seedlings are planted in each m².
How many seedlings are needed for the whole bed?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

11

Find the missing length.

a

a triangle: area 42 cm², a side of 12 cm. The height to that side?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

a trapezoid: area 50 cm², height 5 cm, one base 8 cm. The other base?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

12

A football pitch is a rectangle 105 m long and 68 m wide.

a

Calculate the area of the pitch.

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

Yoav runs 5 laps around the pitch, along its lines.
How many metres does he run?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Formulas: geometry, grade 7

Angles

The sum of angles – the ray $\displaystyle BD$ runs inside $\displaystyle \angle ABC$
$\displaystyle \angle ABC$ $\displaystyle =$ $\displaystyle \angle ABD+\angle DBC$
The difference of angles
$\displaystyle \angle DBC$ $\displaystyle =$ $\displaystyle \angle ABC-\angle ABD$
The bisector $\displaystyle BD$ cuts $\displaystyle \angle ABC$ into two equal angles
$\displaystyle \angle ABD=\angle DBC=\frac{\angle ABC}{2}$
Adjacent angles
$\displaystyle \alpha+\beta=180^{\circ}$
Vertical angles are equal
$\displaystyle \alpha=\gamma$
The angles around a point
$\displaystyle \alpha+\beta+\gamma+\delta=360^{\circ}$

The angles of a triangle and a quadrilateral

The angles of a triangle
$\displaystyle \alpha+\beta+\gamma=180^{\circ}$
The two acute angles of a right triangle
$\displaystyle \alpha+\beta=90^{\circ}$
In an isosceles triangle the base angles are equal
$\displaystyle \angle B=\angle C$ $\displaystyle AB=AC$
In an equilateral triangle all the angles are equal
$\displaystyle \alpha=\beta=\gamma=60^{\circ}$
The angles of a quadrilateral
$\displaystyle \angle A+\angle B+\angle C+\angle D=360^{\circ}$

The perimeter and area of a rectangle and a square

The area of a rectangle – $\displaystyle a$ , $\displaystyle b$ two sides that meet at a vertex
$\displaystyle S$ $\displaystyle =$ $\displaystyle a\cdot b$
The perimeter of a rectangle
$\displaystyle P$ $\displaystyle =$ $\displaystyle 2\cdot(a+b)$
The area of a square – $\displaystyle a$ the side
$\displaystyle S$ $\displaystyle =$ $\displaystyle a^2$
The perimeter of a square
$\displaystyle P$ $\displaystyle =$ $\displaystyle 4\cdot a$

The areas of polygons

The area of a parallelogram – $\displaystyle h_a$ the height to the side $\displaystyle a$
$\displaystyle S$ $\displaystyle =$ $\displaystyle a\cdot h_a$
The area of a triangle – $\displaystyle h_a$ the height to the side $\displaystyle a$
$\displaystyle S$ $\displaystyle =$ $\displaystyle \frac{a\cdot h_a}{2}$
The area of a right triangle – $\displaystyle a$ , $\displaystyle b$ the legs
$\displaystyle S$ $\displaystyle =$ $\displaystyle \frac{a\cdot b}{2}$ $\displaystyle \angle C=90^{\circ}$
The area of a trapezoid – $\displaystyle a$ , $\displaystyle b$ the bases, $\displaystyle h$ the height
$\displaystyle S$ $\displaystyle =$ $\displaystyle \frac{(a+b)\cdot h}{2}$

The box and the cube

The surface area of a box – $\displaystyle a$ the length, $\displaystyle b$ the width, $\displaystyle c$ the height
$\displaystyle S$ $\displaystyle =$ $\displaystyle 2(ab+bc+ac)$
The surface area of a cube – $\displaystyle a$ the edge
$\displaystyle S$ $\displaystyle =$ $\displaystyle 6a^2$
The volume of a box
$\displaystyle V$ $\displaystyle =$ $\displaystyle a\cdot b\cdot c$
The volume of a cube
$\displaystyle V$ $\displaystyle =$ $\displaystyle a^3$