PSEB Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.1
PSEB Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.1
PSEB 9th Class Maths Solutions Chapter 12 Heron’s Formula Ex 12.1
Question 1.
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral 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?
Answer:
In equilateral ∆ ABC, the length of each side is a.
Question 2.
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see the given figure). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
Question 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” (see the given figure). If the sides of the wall are 15 m, 11m and 6 m, find the area painted in colour.
Question 4.
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Answer:
Question 5.
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Answer:
Suppose the sides of the triangle measure 12x cm, 17x cm and 25x cm.
Perimeter of a triangle = Stun of three sides
∴ 540 = 12x + 17x + 25x
∴ 540 = 54x
∴ x = 10
Then, the measures of the sides of the triangle are,
a = 12 × 10 = 120 cm,
b = 17 × 10 = 170 cm and
c = 25 × 10 = 250 cm.
Now, s – a = 270 – 120 = 150 cm,
s – b = 270 – 170 = 100 cm and
s – c = 270 – 250 = 20 cm.
Area of a triangle
Question 6.
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Answer:
Let, the sides of the isosceles triangle be a = 12 cm, b = 12 cm and c cm.
Perimeter of triangle = Sum of three sides
∴ 30 = 12 + 12 + c
∴ 30 = 24 + c
∴ c = 6 cm
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