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

Area of square of side A is$A^2$

Area of given square = 10 $\times$ (10)

= 100 $m^2$

Area of a rectangle whose length and breadth are A m and B m respectively is A $\times$ B

Area of given rectangle = 11 $\times$ 9

= 99 $m^2$
100 is greater than 99.

Hence, Square has greater area compared to the given rectangle.

Formula: 1 Mark
Answer: 1 Mark

Given that
The diameter of a circle is 10m.
Area of the circle whose radius is R  is $\pi \times (R{)}^2$

Radius of the given circle = $\frac{10}{2}$

= 5m

Area of the given circle = $\pi \times (5{)}^2$

= 78.5$m^2$

= 785000${cm}^2$

Area of the required circle is 785000${cm}^2$

Formula: 1 Mark
Answer: 1 Mark

Given that
The circumference of a circle = 70 m 
Let the radius of the circle be 'R' m

Circumference of given circle is 2$\pi$R

2$\pi$R = 70

R = $\frac{35}{\pi }$

Area = $\pi \times (\frac{35}{\pi }{)}^2$

= 389.77$m^2$
The area of the circle is 389.77$m^2$.

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.

Process : 1 Mark
Result : 1 Mark

Perimeter of the parallelogram = 2( side + base )

                                              = 2(10+9) =38 m

  Area of the parallelogram = base $\times$ (height)

                                        = 9 $\times$ (5) = 45 $m^2$

Steps: 2 Marks
Answer: 1 Mark

Given side of a square = 8 cm

If 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$\times$(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 = 2$\pi$R
2$\pi$R = 24
R = $\frac{12}{\pi }$m
R = 3.81 m
The radius of the circle is 3.81 m.

Formula: 2 Marks
Answer: 1 Mark

Let the side of given square be A cm

Area of the given square = $A^2$

Radius of the given circle = $\frac{A}{2}$ cm

 Area of the circle = $\left(\pi \right)(\frac{A}{2}{)}^2$

                           = $\frac{\pi }{4}\times \left(A^2\right)$

                           = 0.785$A^2$
$A^2$$>0.785$$A^2$

So square has more area compared with circle

Steps: 2 Marks
Answer: 1 Mark

Given that 
The length of each side of a square = 4 m
Area of the given square  = $(4{)}^2$

                                        = 16$m^2$
As per the question, the ratio of length and breadth of the rectangle is 2

Area of the rectangle is given = 16 $m^2$

The area of the rectangle whose length is L m and breadth is B m is L $\times$ B m²

     L = 2B ( as per question)

   2B $\times$ B = 16

     B = 2 $\times \sqrt{2}$m

So, L = 2(2 $\times \sqrt{2}$m)

         = 4 $\times \sqrt{2}$m
So, the length of the rectangle is 4 $\times \sqrt{2}$m.

Formula: 1 Mark
Steps: 1 Mark
Application: 1 Mark
Answer: 1 Mark
Given that
Area of a parallelogram=$48c{m}^2$
The parallelogram is divided into two congruent triangles. 

Area of parallelogram = 2(Area of triangle)
Area of triangle = $\frac{48c{m}^2}{2}=24c{m}^2$
Area of triangle = $\frac{1}{2}\times \text{base}\times \text{height}$
$24c{m}^2=\frac{1}{2}\times \text{base}\times 4cm$
base = 12 cm

So, measure of base of the triangle is 12 cm.

Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

According to the question, if base = 12 cm and height = 5 cm
So, area = base $\times$ height = 12 $\times$ 5 = 60 $c{m}^2$

Now​, if base = 8 cm and now we know that area of a parallelogram is 60 $c{m}^2$​

So, Distance between 8 cm sides =  $\frac{60}{8}$ = 7.5 cm
So, the distance between the 8 cm sides is 7.5 cm.

Steps: 3 Marks
Answer: 1 Mark

The given square has a length of 4 m

Area of the Triangle = 0.5 $\times$ 4 $\times$ 4 = 8 $m^2$
The radius inscribed within the square has radius of $\frac{4}{2}=2m$
Area of the given circle = $\pi$ $\times$ $2^2$ =12.56 $m^2$
Circle has a greater area compared to triangle.
Difference between the area of the circle and triangle = 4.56 $m^2$

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 = $4\times x$


The circle will have the same perimeter as that of the square = $4\times x$ metres
Circle will be having a radius(r) = $\frac{4x}{2\pi }$
Area of the Circle so formed 
= $\pi \times \left(\frac{4x}{2\pi }\right)\frac{4x}{2\pi }{m}^2=\frac{4x^2}{\pi }$

The circle which is half cut has a circumference of 2$x$.
Square bent from half circle has the circumference of 2$x$ meters.
Side of the square = $\frac{2x}{4}$
 Area of the square = $\frac{x^2}{4}$
Putting x = 2
We get the area of the circle
= $\frac{4}{\pi }\times 2^2$  = 5.09 $m^2$

The area of the square = $\frac{4}{4}$ = 1$m^2$

The difference between the area of the circle and the area of the square
= 5.09 - 1 = 4.09 $m^2$

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=$\pi \times (r{)}^2{m}^2$

Area of the given circle =$\pi \times (4{)}^2{m}^2$
= $\left(3.14\right)\times \left(16\right)m^2$
=$50.24m^2$
The perimeter of a circle= $2\times \pi \times r$
                                       =$2\times \pi \times 4$
                                       =25.14 m

So, the area of the given circle is $50.24m^2$, and the perimeter is 25.14 m.

Construction: 1 Mark
Application: 2 Marks
Answer: 1 Mark

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

$So,FR=\frac{DQ}{2}$

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

Area of ABCD = $AB\times DQ$

Area of $ABEF=AB\times FR=AB\times \left(\frac{DQ}{2}\right)=\frac{1}{2}\times \left(AreaofABCD\right)=\frac{1}{2}\times 54=27$ square units.