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)

Illustration 2 for 1_Find_the_area_of_below_shape

(2) Find the Area of below Shape

(a)

Illustration 3 for 2_Find_the_area_of_below_shape

(3) Find the Area of below Shape

(a)

Illustration 4 for 3_Find_the_area_of_below_shape

(4) Find the Area of below Shape

(a)

Illustration 5 for 4_Find_the_area_of_below_shape

(5) Find the Area of below Shape

(a)

Illustration 6 for 5_Find_the_area_of_below_shape

(6) Find the Area of below Shape

(a)

Illustration 7 for 6_Find_the_area_of_below_shape

(7) Find the Area of below Polygon

(a)

Illustration 8 for 7_Find_the_area_of_below_polygon

Where,

(8) Find the Area of below Quadrilateral

(a)

Illustration 9 for 8_Find_the_area_of_below_quadrilateral

Where

(9) Find the Area of below Quadrilateral

(a)

Illustration 10 for 9_Find_the_area_of_below_quadrilateral

Where

(10) Find the Area of below Polygon

(a)

Illustration 11 for 10_Find_the_area_of_below_polygon

Where

(11) Find the Circumference of a Circle Whose Area is 961.625 Cm2. (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)

Illustration 12 for 17_Find_the_area_of_shaded_reg …

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

(a)

Illustration 13 for 18_Find_the_area_of_shaded_reg …

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)

Illustration 14 for 19_Find_the_area_of_shaded_reg …

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

(a)

Illustration 15 for 20_Find_Area_of_Shaded_region_ …

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.
Illustration 16 for Answers_and_Explanations
  • 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.
Illustration 17 for Answers_and_Explanations
  • 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.
Illustration 18 for Answers_and_Explanations
  • 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,
Illustration 19 for Answers_and_Explanations

  • 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.
Illustration 20 for Answers_and_Explanations
  • 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.
Illustration 21 for Answers_and_Explanations

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,
Illustration 22 for Answers_and_Explanations
  • So, area of shaded Part

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