Page 144 - Maths Skills - 7

142 Maths

Example 2: Find the area of a triangle whose altitude is 8 cm and base 10 cm.
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Solution: Area of triangle = × base × altitude = × 10 cm × 8 cm = 40 cm .
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Example 3: The base of an isosceles triangle is 12 cm and its perimeter is 30 cm. Find its area.
Solution: We know that an isosceles triangle has two equal sides.
Let each side be x units.
\ (x + x + 12 cm) = 30 cm [Q Perimeter = 30 cm]
⇒ 2x = 18 cm
⇒ x = 9 cm

Now, draw altitude AD ^ BC.

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Altitude (AD) = AB − BD = 9 − 6 cm
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\ Area = × base × height (or altitude)
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= × 12 cm × 81 36− cm
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= × 12 cm × 45 cm = 18 5 cm .
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Exercise 8.5

1. Find the area of the triangle having the following dimensions.
(i) altitude = 20 m, base = 12 m (ii) altitude = 15 m, base = 10 m
(iii) altitude = 12 m, base = 18 m (iv) altitude = 10 m, base = 12.5 m

2. The base of an isosceles triangle is 10 cm and one of its sides is 8 cm. Find the area of the triangle.
3. The area of a right angled triangle is 62 cm . If one of the sides containing right angle is 12.4 cm, then
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find the other sides.
4. Find the area of an isosceles triangle if its base is 16 cm and one of its equal sides is 17 cm long.

5. The base of an isosceles triangle is 10 cm, if its perimeter is 36 cm, then find its area.
6. The area of a triangle is equal to the area of a square having side 70 m. Find the side of the triangle
whose corresponding altitude is 98 m.

7. If the area of an equilateral triangle is 16 3 square units, then find the measure of its sides.
8. Find the length of altitude of an equilateral triangle of sides 20 cm each.

9. Find the altitude of a triangle having base 12 units and area 48 square units.
10. The base of a triangular field is 4 times its height. If the cost of cultivating the field is ` 5000, at the rate
of ` 1 per m , then find the height and base of the field.
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11. The height and base of a triangular field are 250 m and 200 m respectively. Find the cost of levelling the
field at ` 0.50 per metre .
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12. Find the area of an equilateral triangle having the following sides.
(i) 8 cm (ii) 12 cm (iii) 10.2 cm