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NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula are prepared by CBSE student eCARE expert to score good marks in class 9. This chapter contain many topics which are very important to score good in class 9. There are some important topic/Activity mentioned below:
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
Solution:
Let the given field is in the form of a trapezium ABCD such that parallel sides are AB = 10 m and DC = 25 m
Non-parallel sides are AD = 13 m and BC = 14 m.
We draw BE || AD, such that BE = 13 m.
The given field is divided into two shapes (i) ?BCE, (ii) parallelogram ABED For ?BCE:
Sides of the triangle are a = 13 m, b = 14 m, c = 15 m
(ii) For parallelogram ABED:
Let the height of the ?BCE corresponding to the side EC be h m.
Area of a triangle = 12 x base x height
∴ 12 x 15 x h = 84
⇒ (10 + 82×215 = 565
Now, area of a parallelogram = base x height
= (10 x 565) = (2 x 56) m2 = 112 m2
So, area of the field
= area of ?BCE + area of parallelogram ABED
= 84 m2 + 112 m2 = 196 m2
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Some questions are asked by class 9 students related to Maths
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?
Solution:
Let each side of the equilateral triangle be a.
Semi-perimeter of the triangle,
Ex 12.1 Class 9 Maths 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 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?
Solution:
Let the sides of the triangular will be
a = 122m, b = 12cm, c = 22m
Semi-perimeter, s = a+b+c2
(122+120+224)m = 2642 m = 132m
The area of the triangular side wall
Rent for 1 year (i.e. 12 months) per m2 = Rs. 5000
∴ Rent for 3 months per m2 = Rs. 5000 x 312
= Rent for 3 months for 1320 m2 = Rs. 5000 x 312 x 1320 = Rs. 16,50,000.
Ex 12.1 Class 9 Maths Question 3.
There is a slide in a park. One of its side Company hired one of its walls for 3 months.walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see figure). If the sides of the wall are 15 m, 11 m and 6m, find the area painted in colour.
Solution:
Let the sides of the wall be
a = 15m, b = 11m, c = 6m
Semi-perimeter,
Thus, the required area painted in colour
= 20√2 m2