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

### Question 1

Given a square of side 10m and a rectangle of length 11m and breadth 9m. Which one has more area?

[1 MARK]

#### SOLUTION

Solution :

Area of square of side A isA2Area of given square = 10 × (10)

= 100 m2

Area of a rectangle whose length and breadth are A m and B m respectively is A × B

Area of given rectangle = 11 × 9

= 99 m2

100 is greater than 99.Hence, Square has greater area compared to the given rectangle.

### Question 2

Find the area of the circle whose diameter is 10m. Express your answer in cm2. [2 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Answer: 1 Mark

Given that

The diameter of a circle is 10m.

Area of the circle whose radius is R is π×(R)2Radius of the given circle = 102

= 5m

Area of the given circle = π×(5)2

= 78.5m2

= 785000cm2

Area of the required circle is 785000cm2

### Question 3

A circle has a circumference of 70 meters. Find its area. [2 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Answer: 1 Mark

Given that

The circumference of a circle = 70 m

Let the radius of the circle be 'R' mCircumference of given circle is 2πR

2πR = 70

R = 35π

Area = π×(35π)2

= 389.77m2

The area of the circle is 389.77m2.

### Question 4

Is the figure below a polygon? [2 MARKS]

#### SOLUTION

Solution :Reason: 1 Mark

Answer: 1 Mark

This is a closed figure, but this does not contain any straight lines. Hence, it is not a polygon.

### Question 5

Given the side length as 10m and base length as 9m and height as 5m of a parallelogram. Find the area and its perimeter. [2 MARKS]

#### SOLUTION

Solution :Process : 1 Mark

Result : 1 Mark

Perimeter of the parallelogram = 2( side + base )= 2(10+9) =38 m

Area of the parallelogram = base × (height)

= 9 × (5) = 45 m2

### Question 6

Find the missing values: [3 MARKS]

BaseHeightArea of triangle15 cm…87 cm2…31.4 mm1256 mm222 cm…170.5 cm2

#### SOLUTION

Solution :Blanks : 1 Mark each

We know that the area of triangle= 12×base×height

In first row, base=15 cm and area = 87cm2

∴ 87=12×15×height ⇒ height=87×215=11.6 cm

In second row, height=31.4 mm and area =1256 mm2

∴ 1256=12×base×31.4 ⇒ base=1256×231.4=80 mm

In third row, base=22 cm and area =170.5 cm2

∴ 170.5=12×22×height

⇒ height=170.5×222=15.5 cm

Thus, the missing values are:

BaseHeightArea of triangle15 cm11.6 cm87 cm280 mm31.4 mm1256 mm222 cm15.5 cm170.5 cm2

### Question 7

A square of side 8 m is cut into two equal rectangles along its length. The rectangle is bent in the shape of a circle. Find the radius of the circle. [3 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Answer: 1 Mark

Given side of a square = 8 cmIf it is cut into two equal parts the along the length, then:

the rectangles formed will have the length and breadth as 8 m and 4 m respectively

The perimeter of the rectangle will be 2×(8+4) = 24m

The perimeter of the rectangle will be equal to the circumference of the circle.

The circumference of the circle whose radius is R m = 2πR

2πR = 24

R = 12πm

R = 3.81 m

The radius of the circle is 3.81 m.

### Question 8

The side of a square is equal to twice the radius of the circle. Which of them will have greater area?

[3 MARKS]

#### SOLUTION

Solution :Formula: 2 Marks

Answer: 1 Mark

Let the side of given square be A cmArea of the given square = A2

Radius of the given circle = A2 cm

Area of the circle = (π)(A2)2

= π4×(A2)

= 0.785A2

A2>0.785A2So square has more area compared with circle

### Question 9

The area of the given square and rectangle are same. If the length of each side of the square is 4m, and the ratio of length and breadth of the rectangle is 2. Find the length of the rectangle?

[3 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Answer: 1 Mark

Given that

The length of each side of a square = 4 m

Area of the given square = (4)2= 16m2

As per the question, the ratio of length and breadth of the rectangle is 2Area of the rectangle is given = 16 m2

The area of the rectangle whose length is L m and breadth is B m is L × B m

^{2}L = 2B ( as per question)

2B × B = 16

B = 2 × √2m

So, L = 2(2 × √2m)

= 4 ×√2m

So, the length of the rectangle is 4 ×√2m.

### Question 10

A parallelogram of area 48 cm2 is divided into two congruent triangles. If the height of the triangle is 4 cm, find the length of base of the triangle.

[4 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Steps: 1 Mark

Application: 1 Mark

Answer: 1 Mark

Given that

Area of a parallelogram=48 cm2

The parallelogram is divided into two congruent triangles.

Area of parallelogram = 2(Area of triangle)

Area of triangle = 48 cm22=24cm2

Area of triangle = 12×base×height

24 cm2=12×base×4cm

base = 12 cmSo, measure of base of the triangle is 12 cm.

### Question 11

A parallelogram has sides of length 12 cm and 8 cm. If the distance between the 12 cm sides is 5 cm. Find the distance between 8 cm sides. [4 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Steps: 2 Marks

Answer: 1 Mark

According to the question, if base = 12 cm and height = 5 cm

So, area = base × height = 12 × 5 = 60 cm2Now, if base = 8 cm and now we know that area of a parallelogram is 60 cm2

So, Distance between 8 cm sides = 608 = 7.5 cm

So, the distance between the 8 cm sides is 7.5 cm.

### Question 12

Given two squares of the same length. One square has a triangle in it with its vertices coinciding with three vertices of the square. The other square contains a circle touching all mid points of the sides of the square.Which of these two will have a greater area and what is the difference in the areas if the length of the given square is 4m?

[4 MARKS]

#### SOLUTION

Solution :Steps: 3 Marks

Answer: 1 Mark

The given square has a length of 4 mArea of the Triangle = 0.5 × 4 × 4 = 8 m2

The radius inscribed within the square has radius of 42=2m

Area of the given circle = π × 22 =12.56 m2

Circle has a greater area compared to triangle.

Difference between the area of the circle and triangle = 4.56 m2

### Question 13

A square of side 'x' meters is bent in the form of a circle and later this circle is cut into two equal halves. One half is bent to form a square. Find the difference in the areas of the circle and the square bent from the half cut circle if x = 2. [4 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Application: 2 Marks

Answer: 1 Mark

Given that

A square of side 'x' meters is bent into a circle.

The perimeter of the square = 4×x

The circle will have the same perimeter as that of the square = 4×x metres

Circle will be having a radius(r) = 4x2π

Area of the Circle so formed

= π×(4x2π)4x2πm2=4x2π

The circle which is half cut has a circumference of 2x.

Square bent from half circle has the circumference of 2x meters.

Side of the square = 2x4

Area of the square = x24

Putting x = 2

We get the area of the circle

= 4π×22 = 5.09 m2

The area of the square = 44 = 1m2

The difference between the area of the circle and the area of the square

= 5.09 - 1 = 4.09 m2

### Question 14

A man runs in a circular path. He runs towards the center from the circumference and after reaching the center he suddenly changes his direction from his original path at 180 degrees to the original direction and stopped when he reached the circumference. Find the area and perimeter of the circle, given that, the man ran 8 meters in the above-described path? [4 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Steps: 2 Marks

Answer: 1 Mark

Given that

Total distance travelled by the man = 8 m

The man reached toward the center from the circumference to center and back to the center from the circumference.

So, the total distance covered by him is equal to twice the radius of the circle.

Let 'r' be the radius of the circle.So, 2r = 8, r = 4

We know that area of the cicle is given by, Area=π×(r)2m2Area of the given circle =π×(4)2m2

= (3.14)×(16)m2

=50.24m2

The perimeter of a circle= 2×π×r

=2×π×4

=25.14 m

So, the area of the given circle is 50.24m2, and the perimeter is 25.14 m.

### Question 15

If the area of parallelogram ABCD is 54 square units, what is the area of parallelogram ABEF? [Given: O and P are the midpoints of AD and BC respectively]

[4 MARKS]

#### SOLUTION

Solution :Construction: 1 Mark

Application: 2 Marks

Answer: 1 Mark

O and P are the midpoints of AD and AC respectively.

So, FR=DQ2

Also, AB || CD and AB || EF. This implies that EF || CD.

Area of ABCD = AB×DQ

Area of ABEF=AB×FR=AB×(DQ2)=12×(Area of ABCD)=12×54=27 square units.