NCERT Class 9 Solutions: Heron's Formula (Chapter 12) Exercise 12.2 Part 1
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Q1 A park, in the shape of a quadrilateral ABCD, has . How much area does it occupy?
Solution:
Given a quadrilateral ABCD with, .
Construction: Join diagonal AD
To find the area of quadrilateral we can add the areas of two trianlges. In, by applying Pythagoras theorem,
Also since triangle is right triangle, Area of Now, semi perimeter of
Using heron's formula, area of





(approx.)
Area of quadrilateral
Q2 Find the area of a quadrilateral ABCD in which
Solution:
Given a quadrilateral ABCD,
We can calculate the area of the two triangles by using heroes’ formula on the two triangles. However we can make things simple by first proving that that is a right triangle. Let’s see if it satisfies Pythagoras theorem,
Thus, is a right angled at C. Area of
Now, semi perimeter of
Using heron's formula, area of





(approx.)
Finally, area of quadrilateral