NCERT Class 9 Solutions: Heron's Formula (Chapter 12) Exercise 12.2 Part 1

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Herons formula with semi-perimeter

Herens Formula in Two Parts

Herons formula with semi-perimeter

Q-1 A park, in the shape of a quadrilateral ABCD, has . How much area does it occupy?

Solution:

Quadrilateral ABCD

Quadrilateral ABCD, ∠B=90°,CA=9m,AB=12m,BD=5mandCD=8

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

Q-2 Find the area of a quadrilateral ABCD in which

Solution:

Quadrilateral ABCD

Quadrilateral ABCD with CD=3cm,CB=4cm,CD=4cm,AD=5cmandBD=5cm.

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