# Free Perimeter and Area 02 Practice Test - 7th grade

The perimeter of a circle with a diameter = '14 cm' is equal to 88 cm.

A. True
B. False

#### SOLUTION

Solution : B

Here, the diameter is 14 cm, so radius is equal to 7 cm.
The perimeter of a circle with a radius 'r' units = 2πr.
Hence, perimeter of the given circle is equal to
227×2×7
= 44 cm

What is the perimeter of the given polygon (in centimeters) is ___ cm. #### SOLUTION

Solution :

To find the perimeter in centimeters, we have to convert all the dimensions into centimeters.

1500mm=150010cm=150 cm

2m=2×100cm=200cm

500mm=50010 cm=50 cm

1m=1×100cm=100cm. So, after converting all the dimensions to centimeters, the lengths of the sides of polygon are as follows: Perimeter of the polygon (in cm) = (100 + 150 + 50 + 200 + 50 + 100) cm = 650 cm

In the following figure, the area of the total cloth required is 80 cm2 and the area of the yellow cloth required is 60 cm2. If the red colored parts are congruent to each other and the blue cloth is 110th of the yellow cloth, what is the area of the red cloth required? A.

6 cm2

B.

8 cm2

C.

12 cm2

D.

14 cm2

#### SOLUTION

Solution : D Given that the area of the blue cloth = 110 of area of yellow cloth

110 of 60 cm2=6 cm2

Since area of the total cloth = Area of the yellow cloth + Area of the blue cloth + Area of the red cloth required,

Area of the red cloth required = Area of the total cloth - Area of the yellow cloth -  Area of the blue cloth

80 cm260 cm26 cm2=14cm2

Thus, area of the red cloth = 14cm2

If the edge length of a square is a units, the area of the square is  a22 square units.

A.

True

B. False

#### SOLUTION

Solution : B

The area of a square is given by squaring its edge length. So the area of the given square is a2.

Statement 1: The area of a quarter circle is one-fourth of that of a circle with same radius.

Statement 2: The circumference of a quarter circle is one-fourth of that of a circle with same radius.

A.

Both the statements are true

B.

Statement 1 is true and statement 2 is false

C.

Statement 1 is false and statement 2 is true

D.

Both the statements are false

#### SOLUTION

Solution : B

The area of a quarter circle is one-fourth of that of the complete circle because the area is the region enclosed. For a semi-circle, it is half of the total area and for quarter circle, it is one-fourth. So, area of a quarter circle with radius r=πr24

The circumference is the length of the boundary. For a quarter circle with radius r, circumference is given by  (πr2)+2r.

So, statement 1 is true and statement 2 is false.

A car has a tyre of diameter 28 cm. ___ km is covered by the car if the tyre rotates 150 times. (Use π = 22/7)

#### SOLUTION

Solution :

Circumference of a circle of radius r cm = 2πr cm
Thus, circumference of the tyre = 2πr = Distance covered in each rotation

i.e., Distance covered in 1 rotation = 2×π×14 = 88 cm

Distance covered in 150 rotation = 88 × 150 = 13200 cm = 0.132 km

The area of one of the most common Indian sweets as per the given dimensions is ___ cm2. #### SOLUTION

Solution :

Area of a parallelogram=base×heightArea of kajubarfi (parallelogram)=(4×3) cm2=12 cm2

Calculate the area of a rectangle whose length and breadth are 12 cm and 8 cm respectively.

A.

96 cm2

B.

192 cm2

C.

196 cm2

D.

48 cm2

#### SOLUTION

Solution : A

The area A of a rectangle is given by:

A=length×breadth
Therefore, for the given rectangle , we have
A=12×8=96cm2

In order to plant 4 plants per meter, how many plants should you buy to edge your garden along the path as in the given figure? A.

25

B.

35

C.

36

D.

30

#### SOLUTION

Solution : D

You can plant 4 plants per meter.
The perimeter of the garden = 1.25m + 3m + .75m + 2.5m = 7.5m

If in 1m 4 plants can be planted, then in 7.5m, 7.5 × 4 = 30 plants can be planted.

So, 30 plants need to be bought.

One fine morning, Ted woke up and found his dad gardening. His dad was planning to fence the garden with plants. How many saplings should he buy so that his dad can fence the garden with 5 plants every 2.5 metres? A.

31

B.

41

C.

62

D.

82

#### SOLUTION

Solution : D

For 2.5 m, number of saplings required = 5

For 1 m, number of saplings required = 52.5 = 2

Ted has to plant 2 plants per metre.

Perimeter of the garden = (10.2 + 11.4 + 10.6 + 8.8) m = 41.0 m = 41 m

For 1 m, Ted needs 2 plants.

So, for 41 m, Ted is going to need = 41 × 2 = 82 saplings.