Page 241 - Start Up Mathematics_7

Example 9: Find the area of each of the following triangles:

A D P
X

3 cm 5 cm 4 cm
3.2 cm 3 cm

B 6 cm C E F Q 5 cm R Y 4 cm Z
(a) (b) (c) (d)
1
Solution: We know, area of triangle = × base × height
2
1
(a) ar (∆ ABC) = × 6 × 3 = 9 cm 2
2
1
(b) ar (∆ DEF) = × 5 × 3.2 = 8.0 cm 2
2
1
(c) ar (∆ PQR) = × 5 × 4 = 10 cm 2
2
1
(d) ar (∆ XYZ) = × 4 × 3 = 6 cm 2
2
Example 10: Find the missing values in the parallelograms:

Parallelogram Base (b) Height (h) Area
(a) 10.3 cm ...... cm 154.5 cm 2

(b) ...... cm 8.4 cm 48.72 cm 2
Solution: We know, area of parallelogram = base × height

2
(a) 154.5 cm = 10.3 cm × h
∴ h = 154.5 = 15 cm
10.3
2
(b) 48.72 cm = b × 8.4 cm
48.72
∴ b = = 5.8 cm
8.4
Example 11: Find the missing values in the triangles:

Triangles Base (b) Height (h) Area
(a) ...... cm 12.3 cm 246 cm 2
(b) 15 cm ...... cm 87 cm 2

(c) 80 mm 31.4 mm ...... mm 2

(d) ...... cm 15.5 cm 170.5 cm 2

1
Solution: We know, area of triangle = × base × height
2
1 492
(a) × b × 12.3 = 246 ⇒ b = = 40 cm
2 12.3
1 174
(b) × 15 × h = 87 ⇒ h = = 11.6 cm
2 15

233