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NCERT Class 9 Mathematics Chapter 10 Herons Formula
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Herons Formula
Chapter – 10
| Exercise 10.1 |
Q.1. A traffic board, indicating ‘SCHOOL AHEAD’, is an equilat- eral triangle with side ‘a’. Find the area of the signal board, using Heron’s Formula. If its perimeter is 180 cm, what will be the area of the signal board?
Ans: ‘a’ = a
‘b’ =a
‘c’ = a
∴ Area of the signal board
Perimeter = 180 cm
∴ Area of the signal board
Alternatively,
Area of the signal board
Q.2. The triangular side walls of a flyover have been used for advertisement. The sides of the walls are 1200 m, 22m and 120 m (see figure). The advertisements yield an earning of Rs. 5000 per m ^ 2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
Ans: a = 122m
b = 22m
c = 120m
1 year = 12 months
∵ Rent for 12 months per m²= Rs. 5000
∴ Rent for 3 months of 1320 m²= Rs(1250x 1320) =Rs.1650000.
Q.3. There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6, find the area painted in colour.
Ans: a = 15
b = 11 m
c = 6 m
∴ Area painted in colour
Q. 4. Find the area of a triangle two sides of which are 18 cm and 10 and the perimeter is 42 cm. cm.
Ans: a = 18cm
b = 10 cm
Perimeter = 42 cm
⇒ a + b + c = 42 ⇒ 18 + 10 + c = 42
⇒ 28 + c = 42 ⇒ c = 42 – 28
c = 14 cm
∴ Area of the triangle
Q. 5. Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. Find its area.
Ans: Let the sides of the triangle be 12k, 17k cm. Then,
Perimeter = 12k + 17k + 25k = 54k
According to the question,
54k = 540
∴ a = 12k = 12 x 10 = 120 cm
b = 17k = 17 x 10 = 170 cm
c = 25k = 25 x 10 = 250 cm
Q. 6. An isosceles triangle has a perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Ans: a = 12 cm
b = 12 cm
Perimeter = 30 cm
⇒ a+b+c=30 ⇒ 12 + 12 + c = 30
⇒ 24+c=30 ⇒ c = 30 – 24
⇒ c = 6 cm
∴ Area of the triangle
Q.7. Find the area of an equilateral triangle whose perimeter is 24 cm.
Ans: Perimeter of equilateral triangle 24 cm
∴ Each side of triangle
∴ Area of triangle
Q.8. The length of hypotenuse of a right angled triangle is 13 and the length of another side is 5cm. Find its area.
Ans: Let, ABC is a right angle triangle. ∠B = 90⁰, then BC = 5cm,
AC = 13cm.
∴ AB² = AC² – BC = 13² – 5² = 169 – 25 = 144
∴ AB = √144 = 12 cm
So, area of the triangle
