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Area

Class 8th Mathematics (old) MHB Solution
Exercise 21
  1. Calculate the area of the rectangle given its length and breadth. (1) 5.2 cm,…
  2. The side of a square is given. Calculate its area. (1) 25 cm (2) 2.8 m (3) 7.2…
Exercise 22
  1. What is the area of a parallelogram whose base is 12 cm and height 7 cm?…
  2. The area of a parallelogram is 26 sq cm. If its base is 6.5 cm, what is its…
  3. The area of a parallelogram is 56 sq cm and its height is 7 cm. What is its…
  4. What is the area of a parallelogram of base 13 cm and height 5 cm?…
  5. The area of a parallelogram is 390 sq cm. If its height is 26 cm, what is its…
Exercise 23
  1. A certain triangular plot has a base of 20 m and a height of 30 m. What is its…
  2. What is the area of a triangle whose base is 18.2 cm and height, 7.5 cm?…
  3. The sides of a right angled triangle forming the right angle are 16 cm and 8 cm.…
  4. A certain triangle has an area of 125 sq cm. If its base is 25 cm, what is its…
  5. A triangle has an area of 11.6 sq cm. If its height is 2.9 cm, what is its base?…
Exercise 24
  1. If the side of an equilateral triangle is 12 cm, what is its area?…
  2. What will be the area of an equilateral triangle of side 30 cm?
Exercise 25
  1. The diagonals of a rhombus are 84 cm and 42 cm long. What is the area of the…
  2. The area of a rhombus is 1280 sq cm. If one of its diagonal is 64 cm long, what…
  3. The lengths of the diagonals of a rhombus are 12 cm and 18 cm. What is the area…
  4. The area of a rhombus is 432 sq cm. If one of the diagonal has a length of 24…
  5. The area of a rhombus is 702 sq cm. If one of its diagonal is 54 cm long, what…
Exercise 26
  1. The lengths of the parallel sides of a trapezium are 8.7 cm and 5.3 cm. If the…
  2. The area of a trapezium is 262.5 sq cm and the perpendicular distance between…
  3. If the area of a trapezium with parallel sides of length 30 cm and 23 cm…
  4. The area of a trapezium is 84.5 sq cm and its height is 6.5 cm. If one of its…
Exercise 27
  1. If the sides of a triangle are 25 cm, 39 cm, and 56 cm, what is the area of this…
  2. How much will it cost to have a triangular field weeded at the rate of Rs 2 per…
  3. If the length of the sides of a triangular plot of land are 20 m, 21 m and 13 m,…
  4. Use Heron’s formula to find the area of an equilateral triangle whose side is…
  5. The □PQRS alongside is the map of a plot of land. Using the given measures, find…
  6. Using the measures given in the figure below, find the area of □EFGH.…
  7. (1) From the measures given in the figure alongside, find the area of Δ ABC. (2)…
  8. In each of the figures below, find the area of the coloured portion. (1) theta…
Exercise 21
Question 1.

Calculate the area of the rectangle given its length and breadth.

(1) 5.2 cm, 2.5 cm

(2) 2.1 m, 1.5 m

(3) 3.5 m, 1.2 m
Answer:

(1) Given :


Length(l) = 5.2 cm


Breadth(b) = 2.5 cm


Area of rectangle = (l × b)


⇒ Area of rectangle = 13 sq. cm


(2) Given :


Length(l) = 2.1 m


Breadth(b) = 1.5 m


Area of rectangle = (l × b)


⇒ Area of rectangle = 3.15 sq. m


(3) Given :


Length(l) = 3.5 m


Breadth(b) = 1.2 m


Area of rectangle = (l × b)


⇒ Area of rectangle = 4.2 sq. m
Question 2.

The side of a square is given. Calculate its area.

(1) 25 cm (2) 2.8 m

(3) 7.2 cm (4) 13.5 m
Answer:

(1) Side of square(s) = 25 cm


Area of square = (s × s) = 625 sq cm


(2) Side of square(s) = 2.8 m


Area of square = (s × s) = 7.84 sq m


(3) Side of square(s) = 7.2 cm


Area of square = (s × s) = 51.84 sq cm


(4) Side of square(s) = 13.5 m


Area of square = (s × s) = 182.25 sq m
Exercise 22
Question 1.

What is the area of a parallelogram whose base is 12 cm and height 7 cm?
Answer:

Area of Parallelogram = (base × height)


Given:


Base(b) = 12 cm


Height(h) = 7 cm


Area of parallelogram = (b × h) = 84 sq cm
Question 2.

The area of a parallelogram is 26 sq cm. If its base is 6.5 cm, what is its height?
Answer:

Given:


Area of parallelogram = 26 sq cm


Base = 6.5 cm


Height =


⇒ Height = 4 cm
Question 3.

The area of a parallelogram is 56 sq cm and its height is 7 cm. What is its base?
Answer:

Given:


Area of parallelogram = 56 sq cm


Height = 7 cm


Base =


⇒ Base = 8 cm
Question 4.

What is the area of a parallelogram of base 13 cm and height 5 cm?
Answer:

Given:


Base(b) = 13 cm


Height(h) = 5 cm


Area of parallelogram = (b × h) = 65 sq cm
Question 5.

The area of a parallelogram is 390 sq cm. If its height is 26 cm, what is its base?
Answer:

Given:


Area of parallelogram = 390 sq cm


Height = 26 cm


Base =


⇒ Base = 15 cm
Exercise 23
Question 1.

A certain triangular plot has a base of 20 m and a height of 30 m. What is its area?
Answer:

Area of triangle =


Given :


Base = 20 m


Height = 30 m


Area of triangle =


⇒ Area of triangle = 300 sq m
Question 2.

What is the area of a triangle whose base is 18.2 cm and height, 7.5 cm?
Answer:

Area of triangle =


Given :


Base = 18.2 cm


Height = 7.5 cm


Area of triangle =


⇒ Area of triangle = 68.25 sq cm
Question 3.

The sides of a right angled triangle forming the right angle are 16 cm and 8 cm. What is its area?
Answer:

Area of triangle =


Given :


Let Base = 16 cm


Height = 8 cm


Area of Right angled triangle =


⇒ Area of triangle = 64 sq cm
Question 4.

A certain triangle has an area of 125 sq cm. If its base is 25 cm, what is its height?
Answer:

Height =


Area of triangle = 125 sq cm


Base = 25 cm


⇒ Height =


⇒ Height = 10 cm
Question 5.

A triangle has an area of 11.6 sq cm. If its height is 2.9 cm, what is its base?
Answer:

Base =


Area of triangle = 11.6 sq cm


Height = 2.9 cm


⇒ Base =


⇒ Base = 8 cm
Exercise 24
Question 1.

If the side of an equilateral triangle is 12 cm, what is its area?
Answer:

Area of an equilateral triangle =


Given:


Side of triangle (a) = 12 cm


Area =


⇒ Area = 36√3 sq cm
Question 2.

What will be the area of an equilateral triangle of side 30 cm?
Answer:

Area of an equilateral triangle =


Given:


Side of triangle (a) = 30 cm


Area =


⇒ Area = 225√3 sq cm
Exercise 25
Question 1.

The diagonals of a rhombus are 84 cm and 42 cm long. What is the area of the rhombus?
Answer:

Area of rhombus =


Length of first diagonal = 84 cm


Length of second diagonal = 42 cm


Area of rhombus =


⇒ Area of rhombus = 1764 sq cm
Question 2.

The area of a rhombus is 1280 sq cm. If one of its diagonal is 64 cm long, what is the length of the other?
Answer:

Length of Diagonal =


Given :


Area of rhombus = 1280 sq cm


Length of one diagonal = 64 cm


Length of Diagonal =


⇒ Length of Diagonal = 40 cm
Question 3.

The lengths of the diagonals of a rhombus are 12 cm and 18 cm. What is the area of the rhombus?
Answer:

Area of rhombus =


Length of first diagonal = 12 cm


Length of second diagonal = 18 cm


Area of rhombus =


⇒ Area of rhombus = 108 sq cm
Question 4.

The area of a rhombus is 432 sq cm. If one of the diagonal has a length of 24 cm, find the length of the other.
Answer:

Length of Diagonal =


Given :


Area of rhombus = 432 sq cm


Length of one diagonal = 24 cm


Length of Diagonal =


⇒ Length of Diagonal = 36 cm
Question 5.

The area of a rhombus is 702 sq cm. If one of its diagonal is 54 cm long, what is the length of the other?
Answer:

Length of Diagonal =


Given :


Area of rhombus = 702 sq cm


Length of one diagonal = 54 cm


Length of Diagonal =


⇒ Length of Diagonal = 26 cm
Exercise 26
Question 1.

The lengths of the parallel sides of a trapezium are 8.7 cm and 5.3 cm. If the perpendicular distance between them is 4.5 cm, what is its area?
Answer:

Area of trapezium =


Given:


Length of one parallel side = 8.7 cm


Length of the other parallel side = 5.3 cm


Height = 4.5cm


Sum of parallel sides = 14 cm


Area of trapezium =


Area of trapezium = 31.5 sq cm
Question 2.

The area of a trapezium is 262.5 sq cm and the perpendicular distance between its parallel sides is 15 cm, what is the sum of its parallel sides?
Answer:

Given:


Area of trapezium = 262.5 sq cm.


Perpendicular distance = 15 cm


Sum of parallel sides =


⇒ Sum of parallel sides = 35 cm
Question 3.

If the area of a trapezium with parallel sides of length 30 cm and 23 cm respectively is 265 sq cm, what is its height?
Answer:

Given:


Area of trapezium = 265 sq cm.


Length of one parallel side = 30 cm


Length of the other parallel side = 23 cm


Sum of parallel side = (30 + 23) = 53 cm


Height =


⇒ Height = 10 cm
Question 4.

The area of a trapezium is 84.5 sq cm and its height is 6.5 cm. If one of its parallel sides is 15.2 cm long, what is the length of the other side?
Answer:

Given:


Area of trapezium = 84. 5 sq cm


Height = 6.5 cm


Length of one parallel side = 15.2 cm


Length of the other parallel side =


⇒ Length of the other parallel side = 10.8 cm
Exercise 27
Question 1.

If the sides of a triangle are 25 cm, 39 cm, and 56 cm, what is the area of this triangle?
Answer:

Given:


Length of one side of the triangle (a) = 25 cm


Length of second side of the triangle(b) = 39 cm


Length of third side of the triangle (c) = 56 cm


Semi perimeter (s) =


According to Heron’s formula


Area of the triangle = √(s(s-a)(s-b)(s-c))


⇒ Area of the triangle = 420 sq cm
Question 2.

How much will it cost to have a triangular field weeded at the rate of Rs 2 per square metre if the length of the field’s sides are 11 m, 61 m and 60 m?
Answer:

Given:


Length of one side of the triangle (a) = 11 m


Length of second side of the triangle(b) = 61 m


Length of third side of the triangle (c) = 60 m


Semi perimeter (s) =


According to Heron’s formula


Area of the triangle = √(s(s-a)(s-b)(s-c))


⇒ Area of the triangle = 330 sq m


Rate of weeding = Rs 2 per sq m


Total cost = (330 × 2) = Rs 660
Question 3.

If the length of the sides of a triangular plot of land are 20 m, 21 m and 13 m, what is its area?
Answer:

Given:


Length of one side of the triangle (a) = 20 m


Length of second side of the triangle(b) = 21 m


Length of third side of the triangle (c) = 13 m


Semi perimeter (s) =


According to Heron’s formula


Area of the triangle = √(s(s-a)(s-b)(s-c))


⇒ Area of the triangle = 126 sq m
Question 4.

Use Heron’s formula to find the area of an equilateral triangle whose side is ‘p’.
Answer:

Given:


Length of side of the triangle = p


Semi perimeter (s) =


According to Heron’s formula


Area of the triangle = √(s(s-a)(s-b)(s-c))


⇒ Area of the triangle =


⇒ Area of the triangle =



Question 5.

The □PQRS alongside is the map of a plot of land. Using the given measures, find its area.
Answer:

Given:


ST = 13 m


QR = 60 m


PQ = 9 m


PS = 40 m


Area of Δ PQS =


⇒ Area of Δ PQS =


⇒ Area of Δ PQS = 180 sq m


Area of Δ QSR =


⇒ Area of Δ QSR =


⇒ Area of Δ QSR = 390 sq m


Area of PQRS = Area of Δ PQS + Area of Δ QSR = 570 sq m
Question 6.

Using the measures given in the figure below, find the area of □EFGH.
Answer:

Given:


GF = 50 m


GH = 34 m


HF = 52 m


Semi perimeter of Δ GHF =


According to Heron’s formula


Area of the triangle = √(s(s-a)(s-b)(s-c))


⇒ Area of the triangle Δ GHF = 816 sq m


Given:


HE = 20 m


EF = 48 m


HF = 52 m


Semi perimeter of Δ EHF =


According to Heron’s formula


Area of the triangle = √(s(s-a)(s-b)(s-c))


⇒ Area of the triangle Δ EHF = 480 sq m


Area of EFGH = Area of the triangle Δ GHF + Area of the triangle Δ EHF = 1296 sq m
Question 7.

(1) From the measures given in the figure alongside, find the area of Δ ABC.

(2) Using Pythagoras’ theorem find the length of side AC.

(3) Find the area of Δ ABC using Heron’s formula.
Answer:

(1) Given:


AB = 12 cm


BC = 5cm


Area of Δ ABC =


Area of Δ ABC = 30 sq cm


(2) According to pythagoras’ theorem:


AB2 + BC2 = AC2


⇒ AC2 = 122 + 52


⇒ AC = 13 cm


(3) Length of one side of the triangle (a) = 5 cm


Length of second side of the triangle(b) = 12 cm


Length of third side of the triangle (c) = 13 cm


Semi perimeter (s) =


According to Heron’s formula


Area of the triangle = √(s(s-a)(s-b)(s-c))


⇒ Area of the triangle = 30 sq cm
Question 8.

In each of the figures below, find the area of the coloured portion.

(1)

(2)

(3)

(4)


Answer:

(1) Δ PQR is an equilateral triangle


Side of triangle (a) = 8 cm


Area of an equilateral triangle =


Area =


⇒ Area = 16√3 sq cm


(2) Given:


AC = 20 cm


BD = 8 cm


Area of ΔABC =


⇒ Area of ΔABC = 80 sq cm


Length of the rectangle or non shaded region = 5 cm


Breadth of the rectangle or non shaded region = 4 cm


Area of the non shaded region = (Length × Breadth) = 20 sq cm


Area of the shaded region = Area of ΔABC- Area of non shaded region or rectangle


⇒ Area of the shaded region = (80-20) = 60 sq cm


(3) Given:


EF = 15 cm


AB = 20 cm


Area of the parallelogram ABCD = (AB × EF) = 300 sq cm


Area of the Δ AEB =


⇒ Area of the Δ AEB = 150 sq cm


Area of the shaded region = Area of the parallelogram ABCD- Area of the Δ AEB


⇒ Area of the shaded region = 150 sq cm


(4) Given:


NE = 18 cm


SE = 12 cm


Area of Δ QNE =


⇒ Area of Δ QNE or the area of shaded region = 108 sq cm