NCERT Solutions Class 9th Maths Chapter – 10 Heron’s Formula Examples

NCERT Solutions Class 9th Maths Chapter – 10 Heron’s Formula Examples

NCERT Solutions Class 9th Maths Chapter – 10 Heron’s Formula

TextbookNCERT
Class9th
SubjectMathematics
Chapter10th
Chapter NameHeron’s Formula
CategoryClass 9th Math Solutions
MediumEnglish
SourceLast Doubt

NCERT Solutions Class 9th Maths Chapter – 10 Heron’s Formula

Chapter – 10

Heron’s Formula

Examples

Example 1 : Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm (see Fig. 10.3).

NCERT Solutions Class 9th Maths Chapter – 10 Heron’s Formula Examples

Solution – Here we have perimeter of the triangle = 32 cm, a = 8 cm and b = 11 cm. Third side c = 32 cm – (8 + 11) cm = 13 cm
So, 2s = 32, i.e., s = 16 cm,
s – a = (16 – 8) cm = 8 cm,
s – b = (16 – 11) cm = 5 cm,
s – c = (16 – 13) cm = 3 cm

Therefore, area of the triangle = √s(-a) (S-c) (s-c)
= 16 x 8 x 5 x 3cm2 8√30 cm2

Example 2 : A triangular park ABC has sides 120m, 80m and 50m (see Fig. 10.4). A gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of `20 per metre leaving a space 3m wide for a gate on one side.

Solution – For finding area of the park, we have
2s = 50 m + 80 m + 120 m = 250 m.
i.e., s = 125 m
Now, s – a = (125 – 120) m = 5 m,
s – b = (125 – 80) m = 45 m,
s – c = (125 – 50) m = 75 m

Example 3 : The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area.

Solution – Suppose that the sides, in metres, are 3x, 5x and 7x (see Fig. 10.5).
Then, we know that 3x + 5x + 7x = 300 (perimeter of the triangle)
Therefore, 15x = 300, which gives x = 20.
So the sides of the triangle are 3 × 20 m, 5 × 20 m and 7 × 20 m
i.e., 60 m, 100 m and 140 m.
Can you now find the area [Using Heron’s formula]?
We have s =60+100+140/2 m = 150 m
and area will be √150(150-60) (150-100) (150-140) m2
= 150x 90x 50 10 m2
=1500√3 m

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