# Grade 8 Perimeter and Area Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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## (1) Find the Area of below Shape

(a)

## (2) Find the Area of below Shape

(a)

## (3) Find the Area of below Shape

(a)

## (4) Find the Area of below Shape

(a)

## (5) Find the Area of below Shape

(a)

## (6) Find the Area of below Shape

(a)

## (7) Find the Area of below Polygon

(a)

Where,

## (8) Find the Area of below Quadrilateral

(a)

Where

## (9) Find the Area of below Quadrilateral

(a)

Where

## (10) Find the Area of below Polygon

(a)

Where

## (11) Find the Circumference of a Circle Whose Area is 961.625 Cm^{2}. (Π ≈ 3.14)

## (12) Find the Ratio of the Areas of Two Circles Whose Circumferences Are in the Ratio 4: 5

## (13) a Bike՚s Tyre Makes 1500 Rotations to Cover 2.355 Km. Find the Diameter of the Tyre. (Π ≈ 3.14)

## (14) a Circular Track Has a Radius of 300 M. A Vikas Completes 14 Rounds of the Track in Three Hours. What Was Her Average Speed of Vikas? (Π = 22/7)

## (15) the Radius of a Circle Was Increased, Due to Which the Circle՚s Area Increase by Four Times. By What Factor Was the Radius Increased?

## (16) a Car in Moving at a Speed of 88 Km/H. How Many Times Per Hour Are Its Wheels, of Diameter 140 Cm Rotating? (Π = 22/7)

## (17) Find the Area of Shaded Region. (Take Π = 22/7 or Π = 3.14)

(a)

## (18) Find the Area of Shaded Region. (Take Π = 22/7 or Π = 3.14)

(a)

Each circle/semi circle having same diameter 7 cm. PQRS is a square.

## (19) Find the Area of Shaded Region. (Take Π = 22/7 or Π = 3.14)

(a)

## (20) Find Area of Shaded Region. (Take Π = 22/7 or Π = 3.14)

(a)

## Answers and Explanations

### Answer 1 (A)

- Given figure is a trapezium quadrilateral.
- And formula for area of trapezium is as below,

- Here

- So, Area of given figure is

### Answer 2 (A)

- As shown below, given figure is made of two equal parallelograms.

- Formula for area of Parallelogram is as below.

- Where ,

- Now, given figure is made of 2 equal parallelograms.
- Hence Area of given figure,

- Area of given figure

### Answer 3 (A)

- Given figure is a parallelogram quadrilateral.
- Figure can be representing as below.

- Formula for Area of Parallelogram is as below

- Where ,

- Hence area of given parallelogram

### Answer 4 (A)

- As shown below, given figure is made two equal trapeziums.

- Formula for area of trapezium is as below,

- Where,

- Given figure is made of two trapezium,
- Area of given figure

- Hence Area of given figure

### Answer 5 (A)

- Given figure is Kite Quadrilateral.
- Formula for Area of Kite is as below.

- Where,

- Area of given figure

### Answer 6 (A)

- As shown below, for the area of rhombus ABCD,

- Where,

- Now as show in figure is a right angle triangle,

- Diagonal AC

- Now, Diagonal BD

- Now,
- Where,

- Area of Given Shape

### Answer 7 (A)

- Given Figure is made of 4 Triangle.
- So, area of Polygon is summation of area of this 4 triangle.

- Area of Polygon PQRST

- Area of :

- Area of :

- Area of :

- Area of

- Now, Area of Polygon PQRST

- Therefore, area of Polygon PQRST is

### Answer 8 (A)

- Given Quadrilateral is made of two Triangle as shown in Figure

- Area of quadrilateral STAR

- Now, Area of ,

- Now, Area of ,

- Now, Area of quadrilateral STAR

- Therefore, area of quadrilateral STAR is

### Answer 9 (A)

- Given Quadrilateral is made of two Triangle as shown in Figure

- Area of quadrilateral FAST

- Now, Area of

- Now, Area of :

- For FS;

- Now,

- Now, Area of quadrilateral FAST

- Therefore, area of quadrilateral FAST is

### Answer 10 (A)

- Given Polygon is made of 4 triangles and one trapezium.
- Area of polygon is summation of all this 4 triangle and one trapezium

- Area of :

- Area of :

- Now,

- Area of :

- Now,

- Area of :

- Area of trapezium NORM:

- Where,

- Now,

### Answer 11 (A)

- Where d is Diameter of Circle.

- Now,
- Where d is Diameter of circle = 35 cm (derived above)

### Answer (12)

- The ratio of circumference of two circle are hence,

- Where

- Now,
- Ratio of Area of this two Circle,

- Hence ratio of the areas of this two circles
**is**

### Answer (13)

- A bike՚s tyre makes 1500 rotations to cover 2.355 km
- So,

- So, we can say that 1.57m is a circumference of bike՚s tyre

- Where

- So, Diameter of Bike՚s tyre is

### Answer (14)

- The circular track has radius
- So, Diameter of Circular Track (d)
- Diameter of Circular Track

- Now, Vikas complete 14 rounds of Track , so he travel total distance

- So, Vikas total travel 26.400 km distance in 3 hours
- Average speed of Vikas

### Answer (15)

- Suppose initially the radius of circle is
- And when Circle՚s area increase by four times its radius become
- Hence,

- When Circle Area Increase Four times than,

- Hence,
**The radius of a circle was Doubled**, due to which the circle՚s area increase by four times

### Answer (16)

- A Car is moving at a speed of 88 km/h.
- Means car is travelling m/h.
- Now Diameter of car՚s wheel (d) is 140 cm
- Now ,

- That means if car travel 4.4 meter than its wheel complete one rotation.

- So, cars wheel rotating
**20,000 times**per hour

### Answer 17 (A)

- There are two figures in give figure.

- Now, as shown in figure given triangle is right angle triangle and its hypotenuse is a diameter of circle (d) .
- So, for right angle triangle,

- Hence Diameter of Given circle is 13 cm
- Now, area of triangle:

- Now, area of circle:

- Now, area of shaded part

### Answer 18 (A)

- Area of Shaded Part

- As shown in figure Side of Square
- So,

- Now,
- Where d is diameter of circle = 7 cm

- Now as shown in below figure there are 3 full circle inside the square.

### Answer 19 (A)

- Area of Shaded part

- Area of Circle:
- Circle having 14 cm diameter (d) .

- Area of Rectangle:
- Long side of rectangle (b)
- Small Side of Rectangle (a)

- Now, area of shaded part

### Answer 20 (A)

- Area of Shaded Part

- Now, Area of Rectangle:
- Long side of rectangle (b)
- Small Side of Rectangle (a)

- Area of Circle:
- Circle having 14 cm diameter (d) .

- Area of Trapezium:
- Long side of Trapezium (a)
- Small Side of Trapezium (b)
- Height of Trapezium

- Now As shown in figure there are one circle , and 2 trapezium in the figure,

- So, area of shaded Part