Page 227 - ICSE Math 8

Example 6: One of the equal sides of an isosceles triangle is 10 m and its perimeter is 32 m. Find the area
of the triangle.
Solution: Let the third side of the triangle be x m. Try These
Perimeter = 32 m 1. Find the area of a triangle with sides
⇒ 10 + 10 + x = 32 13 m, 21 m and 20 m.
⇒ x = 12 2. Find the area and perimeter of an
10 + 10 + 12 equilateral triangle with side 12 cm.
s = 2 m = 16 m 3. Find the perimeter of an equilateral
2
∴ Area of triangle = 16(16 10)(16 10)(16 12) m 2 triangle with area 36 3m .
−
−
−
× × ×
= 1666 4 m 2
4
23 23 2 m
= 2 × ×× ×× 2 2
2
8
= 2 × 3 m 2
4
= 2 × 3 = 48 m 2
EXERCISE 21.2

1. Find the area of a right-angled triangle with hypotenuse 26 cm and a side of length 24 cm.
2. Find the area of a triangle with sides 25 cm, 17 cm and 26 cm. Also, find the height of the triangle
corresponding to the smallest side of the triangle.

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3. The area of an equilateral triangle is 16 3 cm . Find the length of each side and perimeter of the triangle.
4. The base of an isosceles triangular park is 18 m and its equal sides are of length 15 m each. Find the cost
of levelling it at the rate of ` 15 per square metre.
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5. The base and height of a triangle are in the ratio 4 : 7. If the area of the triangle is 126 m , find its base
and height.
6. One of the equal sides of an isosceles triangle is 18 cm and its perimeter is 48 cm. Find the area of the triangle.
7. The sides forming the right angle in a right-angled ∆ABC are 8 cm B
and 6 cm. Find

(a) the length of the hypotenuse (b) area of ∆ABC A C
(c) the length of the altitude corresponding to the hypotenuse D
8. In ∆DEF, FG ⊥ DE and DH ⊥ EF. If DE = 18 cm, F
EF = 20 cm and FG = 7 cm, find DH.
H

D E
G
9. The lengths of the sides of a triangle are in the ratio 3 : 5 : 4 and its perimeter is 72 cm. Find the area of
the triangle.

Area of a Parallelogram D C D C
Area of a parallelogram = base × height h
Any side of a parallelogram can be taken as its base (b) and h E
the length of the corresponding altitude will be its height (h). b
A E b B A B
Area = AB × DE Area = BC × DE

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