Important Questions Class 8 Maths Ganita Prakash – II Chapter 7 Area

Short Questions

Q1. Find the area of a rectangle of length 8 cm and width 5 cm.

Solution:
Area = length × width = 8 × 5 = 40 cm²
Answer: 40 cm²

Q2. Find the area of a triangle with base 10 cm and height 6 cm.

$\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$
Solution:
= ½ × 10 × 6 = 30 cm²
Answer: 30 cm²

Q3. Find the area of a parallelogram with base 9 cm and height 4 cm.

Solution:
Area = base × height = 9 × 4 = 36 cm²
Answer: 36 cm²

Q4. Find the area of a rhombus whose diagonals are 12 cm and 8 cm.

Solution:
Area = ½ × d₁ × d₂
= ½ × 12 × 8 = 48 cm²
Answer: 48 cm²

Q5. Find the area of a trapezium with parallel sides 6 cm and 10 cm, height 5 cm.

Solution:
Area = ½ × height × (sum of parallel sides)
= ½ × 5 × (6 + 10)
= ½ × 5 × 16 = 40 cm²
Answer: 40 cm²

Q6. A square has side 7 cm. Find its area.

Solution:
Area = side² = 7 × 7 = 49 cm²
Answer: 49 cm²

Q7. Find the area of a rectangle whose length is 12 cm and width is 3 cm.

Solution:
Area = 12 × 3 = 36 cm²
Answer: 36 cm²

Q8. Find the area of a triangle with base 15 cm and height 4 cm.

Solution:
Area = ½ × 15 × 4 = 30 cm²
Answer: 30 cm²

Q9. Find the area of a parallelogram with base 11 cm and height 2 cm.

Solution:
Area = 11 × 2 = 22 cm²
Answer: 22 cm²

Q10. Find the area of a rectangle with sides 7 cm and 4 cm.

Solution:
Area = 7 × 4 = 28 cm²
Answer: 28 cm²

Long Questions

Q1. A rectangular field has length 20 m and width 15 m. Find:

(a) Area
(b) Area of one triangular half formed by diagonal

Solution:
(a) Area of rectangle = 20 × 15 = 300 m²

(b) Triangle area = ½ × rectangle area
= ½ × 300 = 150 m²

Answer:
(a) 300 m²
(b) 150 m²

Q2. A trapezium has parallel sides 12 cm and 18 cm, height 8 cm. Find its area.

$\text{Area of trapezium} = \frac{1}{2} \times h \times (a + b)$
Solution:
= ½ × 8 × (12 + 18)
= ½ × 8 × 30
= 4 × 30 = 120 cm²

Answer: 120 cm²

Q3. The diagonals of a rhombus are 16 cm and 10 cm. Find its area.

Solution:
Area = ½ × 16 × 10
= 80 cm²

Answer: 80 cm²

Q4. A triangle has base 14 cm and height 9 cm. Another triangle has the same base but double height. Compare their areas.

Solution:
First triangle:
Area = ½ × 14 × 9 = 63 cm²

Second triangle:
Height = 18 cm
Area = ½ × 14 × 18 = 126 cm²

Comparison:
126 : 63 = 2 : 1

Answer: Second triangle has double area (ratio 2:1)

Q5. A rectangular park is 25 m long and 10 m wide. A path of width 2 m is made inside along all sides. Find the area of the path.

Solution:
Outer rectangle area = 25 × 10 = 250 m²

Inner rectangle:
Length = 25 − 4 = 21 m
Width = 10 − 4 = 6 m

Inner area = 21 × 6 = 126 m²

Area of path = 250 − 126 = 124 m²

Answer: 124 m²