Area Class 8 Worksheet with Answers Maths Chapter 7

Each of our Ganita Prakash Class 8 Worksheet and NCERT Class 8 Maths Chapter 7 Area Worksheet with Answers focuses on conceptual clarity.

Area Worksheet Class 8

Class 8 Maths Area Worksheet

Area Class 8 Ganita Prakash Worksheet

Rectangle and Squares

Ravi and Sanya were in the park one day, discussing their new project for the school fair. The theme was “Creative Geometry,” and they had decided to design a large garden shaped like a square. They needed to divide the space into four equal parts for different activities.

Ravi: I think we can simply divide the square into four smaller squares by drawing two lines from corner to corner. That seems like the easiest method.

Sanya: Hmm, that’s a good idea, but what if we try something more creative? I bet we can divide the square into four equal parts in more ways than one. How about we compress and expand the parts along different edges?

Ravi: That’s interesting! So, you’re suggesting we compress one side and expand the opposite side of each smaller section, but the area stays the same.

Sanya: Exactly! IT we make sure the total area of each part stays the same, it will work. And we can do this in an infinite number of ways!

Question 1.
Answer the following questions:
(a) Imagine you are helping Ravi and Sanya with this project. How would you ensure that the area of each part remains the same, even if the shapes change?
Answer:
Area = length × width

(b) If the sidelength of the square garden is 16 metres, what is the area of the entire garden?
Answer:
256 m²

(c) Sanya divides the square into four equal parts by compressing and expanding along the edges. If the original square has a side length of 16 m, what is the area of each part if the square is divided equally?
Answer:
64 m²

(d) If each of the four equal parts has an area of 25 square metres, what is the sidelength of the original square garden?
Answer:
10 m

(e) What is the area of each triangle in this rectangle?

Answer:
72 m²

(f) Sanya is creating a rangoli art form and needs to calculate how much powder she will need for two different rectangles ‘A’ and ‘B’. ‘A’ has sides of 6 cm and 4 cm, and ‘B’ has sides of 12 cm and 1 cm respectively. Which rectangle needs more powder?
Answer:
A

(g) Using the result from part (f):
(i) Calculate the perimeter of each rectangle.
(ii) Does a rectangle with a larger perimeter always have a larger area? Explain your answer using these rectangles.
Answer:
(i) A : 20 cm, B : 26 cm
(ii) No

Question 2.
Find the missing values of the following figures.
(a)

Answer:
24 m²

(b)

Answer:
6 in, 20 in²

Question 3.
A rectanguLar park has dirnersLons of 20 metres by 10 metres. A path of uniform width is Laid around the park, with the width of the path being 2 metres. What is the area of the path?
Answer:
136 m²

Question 4.
A rectangular park has dimensions of 30 metres by 20 metres. A cross path of 2 metres width runs along both the length and the width of the park. What is the total area of the cross path?
96 metre²

Question 5.
Find the area of the spiral tube shown in the diagram. The tube maintains a consistent width throughout.

Answer:
119 unit²

Triangles

Question 6.
In the given figure, which triangle has a greater area: ΔXDC or ΔYAD?

Answer:
Both will have same area.

Question 7.
Find the area of the following triangles:

Answer:
(a) 90 cm²
(b) 187.5 cm²
(c) 135 cm²
(d) 30.875 cm²

Question 8.
Find the length of AC in the given figure.

Answer:
20 cm

Question 9.
InΔPQR, PR = PQ, and the perpendicular from P to QR meets at point S. If the area of triangle ΔPSQ is 15 sq. units, calculate the area of triangle ∆PQR.
Answer:
30 unit²

Question 10.
Ia the following figure ABCD, BCFE, and DCGH are identical squares. If the area of shaded region is 96 cm², then find the area of each square.

Answer:
76.8 cm²

Question 11.
If D and E are the midpoints of sides AB and AC of triangle AABC, and BC is the base, what fraction of the area of AABC is the area of AADE?

Answer:
\(\frac{1}{4}\)

Area of any Polygon

Question 12.
Find the area of shaded region of the following figures.

Answer:
(a) 39 m²
(b) 135 cm²

Question 13.
What fraction of the total area of the rectangle is the area of the shaded region?

Answer:
\(\frac{1}{2}\)

Parallelogram, Rhombus and Trapezium

Question 14.
Find the area of the following parallelograms:

Answer:
(a) 275 in²
(b) 108 cm²

Question 15.
In parallelogram PQRS, the base SR = 12 cm and the corresponding height QM = 6 cm. Find the area. Also, find the height QN, if the adjacent side PS = 7.5 cm.
Answer:
QN = 9.6 cm, Area = 72 cm²

Question 16.
Find the area of a rhombus whose diagonals are 22 cm and 18 cm respectively.
Answer:
198 cm²

Question 17.
The diagonals of a rhombus are 24 cm and 10 cm. Find the area of the rhombus. If the rhombus has a perimeter of 52 cm, calculate the length of each side.
Answer:
120 cm²

Question 18.
A rhombus has a perimeter of 48 cm, and one of its diagonals measures 16 cm. Calculate the area of the rhombus.
Answer:
64√5 cm²

Question 19.
Find the area of the following trapeziums:

Answer:
(a) 70 cm²
(b) 102 cm²
(c) 70 cm²

Question 20.
In an isosceles trapezium, the lengths of the parallel sides are 10 cm and 15 cm, and the height is 4 cm. If the trapezium is divided into a rectangle and two triangles, calculate the area of each triangle.
Answer:
5 cm²

Question 21.
The area of a trapezium is 1080 cm². If the lengths of its parallel sides are 55.6 cm and 34.4 cm, find the distance between them.
Answer:
24 cm

Question 22.
The area of a trapezium is 384 cm². Its parallel sides are in the ratio 3 : 5 and the perpendicular distance between them is 12 cm. Find the length of each of the parallel sides.
Answer:
24 cm, 40 cm

Question 23.
WXYZ Is a trapezium with XY || WZ. L is the midpoint of YZ. Show that the area of the trapezium WXYZ is equal to the area of ∆WXM.

Question 24.
Express the following lengths in centimetres:
(a) 8.5 in
(b) 8.5 in
Answer:
(a) 30.48 cm
(b) 21.59 cm

Question 25.
It a village occupies 150 acres of land, what is the area in square feet?
Answer:
65,34,000 ft²

Question 26.
If your city covers an area of 250 km², what is its area in square metres
Answer:
25,00,00,000 m²

Work sheet On Area Class 8

A. Choose the correct option.

1. The area of a rectangle with sidelengths of 7 cm and 4 cm is
(a) 28 cm²
(b) 24 cm²
(c) 35 cm²
(d) 21 cm²
Answer:
(a) 28 cm²

2. Which of the following shapes has an area formula as × base × height’?
(a) Square
(b) Rectangle
(c) Triangle
(d) Rhombus
Answer:
(c) Triangle

3. If two triangles share the same base and height, which statement is true?
(a) They must have different areas.
(b) Their areas are equal.
(c) The triangle with the longer base has a larger area.
(d) The triangle with the shorter base has a larger area.
Answer:
(b) Their areas are equal.

4. The area of a rhombus can be calculated using the formula:
(a) base x diagonal
(b) \(\frac{1}{2}\) × base × height
(c) \(\frac{1}{2}\) × product of diagonals
(d) base × widht
Answer:
(c) \(\frac{1}{2}\) × product of diagonals

5. Which of the following statements about the area of a triangle is correct?
(a) The area is always equal to \(\frac{1}{2}\) × base × height.
(b) The area is always calculated using the formula base × height.
(c) The area is calculated only for right-angled triangles.
(d) The area depends on the perimeter of the triangle.
Answer:
(a) The area is always equal to \(\frac{1}{2}\) × base × height.

6. A smartphone screen measures 6-inches in length. If 1 inch = 2.54 cm, what is the length in centimetres?
(a) 15.24 cm
(b) 2.36 cm
(c) 8.54 cm
(d) 12.00 cm
Answer:
(a) 15.24 cm

Directions. (For Q.7 – 8): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

7. Assertion (A): Triangles on the same base and between the same parallels have the same perimeter.
Reason (R): Triangles on the same base and between the same parallels have the same area.
Answer:
(d) Assertion (A) is false but Reason (R) is true.

8. Assertion (A): The area of a parallelogram can be found by taking any side as the base and multiplying by its corresponding height.
Reason (R): A parallelogram can be dissected and rearranged into a rectangle in more than one way.
Answer:
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

B. Fill in the blanks.

1. The formula to find the area of a parallelogram is ______ .
Answer:
base × height

2. The area of a trapezium is calculated using the formula ______ .
Answer:
\(\frac{1}{4}\) x sum of parallel sides x height

3. A rhombus has diagonals of lengths 8 cm and 6 cm. Its area is ______.
Answer:
24 cm²

4. The area of a triangle is half of the product of its ______ and ______.
Answer:
base, height

5. If the height of a rectangle is 5 cm and its area is 30 cm², the length of the rectangle is ______.
Answer:
6 cm

C. State whether the following statements are True (T) or False (F).

1. The area of a rhombus is calculated using the formula \(\frac{1}{2}\) x product of its diagonals.
Answer:
True

2. A triangle with a base of 10 cm and height of 4 cm has an area of 40 cm².
Answer:
False

3. The diagonals of a rhombus always bisect each other at right angles.
Answer:
True

4. The formula for the area of a parallelogram is the same as that for a rectangle.
Answer:
True

5. The area of any polygon can be found by dividing it into smaller triangles.
Answer:
True

D. Solve the following.

Question 1.
The area of a trapezium is 60 cm². Its parallel sides measure 8 cm and. 12 cm. Find the height of the trapezium.
Answer:
6 cm

Question 2.
Find the area of a parallelogram with a base of 8 cm and a height of 5 cm. Then, calculate the area if the height is doubled.
Answer:
40 cm², 80 cm²

Question 3.
Two congruent triangles are formed from a rectangle by drawing a diagonal. If the area of the rectangle is 30 cm2, what is the area of each triangle?
Answer:
15 cm²

Question 4.
A farmer owns a quadrilateral-shaped field. He draws one of its diagonals, which measures 200 m. The  perpendiculars distances from the other two vertices to this diagonal are 80 m and 120 m. Find the area of the field in square metres?
Answer:
20000 m²

Question 5.
A rectangular plot of land is 50 m by 30 m. A concrete path of uniform width 2.5 m is laid around the outside of the plot. A second gravel path of uniform width 2 m is laid inside the plot. Find the cost of laying both paths if concrete costs ₹200 per sq. m and gravel costs ₹120 per sq. m.
Answer:
Cost of Paths: Concrete = ₹ 85,000 Gravel = ₹ 36,480.