Grade 7 Perimeter and Area Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Find the Perimeter of Each Figure

(a)

Illustration 2 for 1_Find_the_perimeter_of_each_figure

(b)

Illustration 3 for 1_Find_the_perimeter_of_each_figure

(2) Find the Area of below Rectangular Figure

(a)

Illustration 4 for 2_Find_the_area_of_below_rectan …

(3) Find the Area of below Rectangular Figure

(a)

Illustration 5 for 3_Find_the_area_of_below_rectan …

(4) Find the Area of below Figure Shaded Region

(a)

Illustration 6 for 4_Find_the_area_of_below_figure …

(5) Find the Area of below Figure Shaded Region

(a)

Illustration 7 for 5_Find_the_area_of_below_figure …

(6) Dev Wants to Fens His Rectangular Farm House of Length 60m and Breadth 40m. What is the Cost of Fencing at the Rate of ₹ 40 Per Meter?

(7) a Wall Has Door of 2m in Height and Breadth 1m. If the Length of Wall is 14m and Breadth is 4m, Find the Cost of Painting the Wall at the Rate of ₹ 15 Per M2

(8) Find the Area of Each Parallelogram Using the Given Base (B) and Height (H)

(a)

(b)

(c)

(d

(9) What is the Base of Parallelogram Whose Area is 460 Sq. Cm and Height is 20 Cm

(10) the Adjacent Sides of a Parallelogram Are 20 M and 8 M. If the Distance between Its Longer Sides is 5 M, Find the Distance between Its Shorter Sides

(11) Answer the Following

(a) What is the area of triangle whose base is 8cm and altitude is 18 cm?

(b) What is the side length of equilateral triangle having area of ?

(12) Find the Area of below Figure

Illustration 8 for 12_Find_the_area_of_below_figure

(13) Find the Area of Shaded Region of below Figure

Illustration 9 for 13_Find_the_area_of_shaded_regi …

(14) the Base of a Triangular Field is Two Times Its Altitude. If the Cost of Cultivating the Field at ₹ 18 Per M2 is ₹ 216, Find the Base of the Field

(15) Find the Circumference of the Circle Whose

(a) Radius is 14 cm

(b) Diameter is 3.5m

(c) Radius is 8.4 cm

(d) Diameter is 42cm

(16) Find the Area of Circle Whose

(a) Radius 14cm

(b) Diameter 2.1m

(17) Find the Radius of the Circle Whose

(a) Circumference is 1.76m

(b) Area is 154 cm2.

(18) if the Diameter of Wheel is 42cm, How Much Distance Does Wheel Cover in 120 Revolution?

(19) if the Area of Circle is 169 Times the Area of Another Circle, What is Ratio of Their Circumference?

Answers and Explanations

Answer 1 (A)

  • Perimeter means length of outline of given figure.
  • To find out perimeter of given figure first we have to find out missing dimension of figure as below,
Illustration 10 for Answers_and_Explanations
  • Missing dimension represent if red color in above figure.
  • Now perimeter of given figure

  • Therefore Perimeter of given figure is

Answer 1 (B)

  • Perimeter means length of outline of given figure.
  • To find out perimeter of given figure first we have to find out missing dimension of figure as below,
Illustration 11 for Answers_and_Explanations
  • Missing dimension represent if red color in above figure.
  • Now perimeter of given figure

  • Therefore Perimeter of given figure is

Answer 2 (A)

  • To find out the area of given figure, first divide the figure in part of rectangle, than find out area of individual rectangle and then do summation area of all rectangle.
  • Given figure divide in part of rectangle as below;
Illustration 12 for Answers_and_Explanations
  • Now Area of Rectangle-1

  • Area of Rectangle-2

  • Area of Rectangle-3

  • Now area of Figure

  • Therefore Area of given figure is

Answer 3 (A)

  • To find out the area of given figure, first divide the figure in part of rectangle, than find out area of individual rectangle and then do summation area of all rectangle.
  • Given figure divide in part of rectangle as below;
Illustration 13 for Answers_and_Explanations
  • Area of Rectangle-1

  • Area of Rectangle-2

  • Area of Rectangle-3

  • Now area of Figure

  • Therefore Area of given figure is

Answer 4 (A)

  • Area of shaded region can be find out by calculating the area of all rectangle and then substitute the area of unshaded region from this.

Illustration 14 for Answers_and_Explanations
  • Now as shown in figure;
  • Area of unshaded rectangle-1

  • Area of unshaded rectangle-1

  • Area of unshaded rectangle-1

  • Now,

  • Area of Shaded region

Answer 5 (A)

  • Area of shaded region can be find out by calculating the area of full figure and then substitute the area of unshaded region from this.
  • To find out area of full figure consider below figure;
Illustration 15 for Answers_and_Explanations
  • Area of shaded rectangle-1

  • Area of shaded rectangle-2

  • Area of shaded rectangle-2

  • Now,

  • From figure Area of unshaded rectangle

  • Now,

  • Therefore Area of shaded region is

Answer (6)

  • Length of rectangular farm house is 60m
  • Breadth of rectangular farm house is 40m

Therefore

  • Now,

  • Therefore, cost of fencing of farm house is ₹ 8000

Answer (7)

  • Given question can be represent as below.
Illustration 16 for Answers_and_Explanations
  • Where the door is installed; not able to paint the wall, hence can paint the wall accept door area.
  • Now;

  • Now,

  • Therefore,

  • Now,

  • Therefore Cost of painting the wall is ₹ 810

Answer 8 (A)

  • Base (b) of parallelogram
  • Height (h) of parallelogram

  • Therefore Area of parallelogram is

Answer 8 (B)

  • Base (b) of parallelogram
  • Height (h) of parallelogram

  • Therefore Area of parallelogram is

Answer 8 (C)

  • Base (b) of parallelogram
  • Height (h) of parallelogram

  • Therefore Area of parallelogram is

Answer 8 (D)

  • Base (b) of parallelogram
  • Height (h) of parallelogram

  • Therefore Area of parallelogram is

Answer (9)

  • Area of parallelogram
  • Height of parallelogram
  • Now,

  • Therefore Base of parallelogram is 23 cm

Answer (10)

  • Given problem represented in figure as below,
Illustration 17 for Answers_and_Explanations
  • From figure
  • Base of parallelogram
  • Height of parallelogram
  • Now,

  • Now, for other side
  • Base of parallelogram
  • Height of parallelogram
  • Area of parallelogram
  • Now,

  • Therefore, Distance between shorter sides

Answer 11 (A)

  • Given that Base of triangle
  • Altitude of triangle height of triangle
  • Now

  • Therefore, Area of triangle

Answer 11 (B)

  • Suppose Side length of equilateral triangle
  • Area of equilateral triangle
  • Formula for area of equilateral triangle is;

  • Therefore, The equilateral triangle whose area is have side length

Answer (12)

  • Given figure is made of two figure as shown in below figure
  • One is rectangle and other is triangle

Illustration 18 for Answers_and_Explanations
  • For rectangle
  • Length of rectangle
  • Breadth of rectangle

  • Now for triangle
  • Base of triangle
  • Height of triangle

  • Now,

  • Therefore Area of figure

Answer (13)

  • Given figure have two part, the one full figure out line form a parallelogram and inside parallelogram there is triangle.
Illustration 19 for Answers_and_Explanations
  • Therefore,

  • Now for area of parallelogram
  • Base of parallelogram
  • Height of parallelogram

  • Now for area of triangle
  • Base of triangle
  • Height of triangle

  • Now,

  • Therefore, Area of shaded region of figure

Answer (14)

  • Given that the base of a triangular field is two times its altitude
  • Suppose altitude of triangle
  • Than Base of triangle
  • Rate of cultivating the field is 18 per sq. m
  • And total cost of cultivating the triangle shape field is ₹ 216.
  • Now,

  • Given that field is of triangular shape
  • Therefore Area of triangle Cultivating area

  • Therefore;
  • Altitude of triangle
  • Base of triangle

Answer 15 (A)

  • Given that Radius of circle is 14 cm

  • Therefore Circumference of circle having radius 14 cm is 88cm

Answer 15 (B)

  • Given that Diameter of circle is 3.5 m
  • Radius of circle
  • Radius of circle

  • Therefore Circumference of circle having diameter 3.5 m is 11m

Answer 15 (C)

  • Given that Radius of circle is 8.4 cm

  • Therefore Circumference of circle having radius 8.4 cm is 52.8cm

Answer 15 (D)

  • Given that Diameter of circle is 42 cm
  • Radius of circle
  • Radius of circle

  • Therefore Circumference of circle having diameter 42cm is 132 cm

Answer 16 (A)

  • Given that radius of circle is 14cm
  • Diameter of circle
  • Diameter of circle

  • Therefore area of circle having radius 14 cm is

Answer 16 (B)

  • Given that Diameter of circle is 2.1 m

  • Therefore area of circle having diameter 2.1 m is

Answer 17 (A)

  • Circumference of circle is 1.76m

  • Therefore Circle whose circumference is 1.76 m have radius 1.12m

Answer 17 (B)

  • Area of circle is

  • Now,
  • Radius of circle
  • Radius of circle
  • Therefore Circle whose Area is 154 cm have radius 7 cm

Answer (18)

  • Diameter of wheel is 42 cm
  • In one revolution wheel cover distance equals to its circumference.

  • Therefore,

  • Therefore wheel cover 15840cm distance in 120 revolution.

Answer (19)

  • Given that the area of circle is 169 times the area of another circle
  • suppose
  • Now,

  • Now,
  • Ratio of circumference;

  • Therefore Ratio of circumference is 13.

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