A park, in the shape of a quadrilateral ABCD has angle B=900 , AB=9m, BC=40m, CD=15m, DA=28m. How much area does it occupy?

Given:

In quadrilateral ABCD, angle B=90° , AB=9m, BC=40m, CD=15m, DA=28m.

To find:

The area of the quadrilateral ABCD.

Solution:

In quadrilateral ABCD, draw a diagonal AC.

Using Pythagoras theorem in triangle ABC, we get

Taking square root on both sides, we get

Area of the triangle ABC is:

So, the area of the triangle ABC is 180 square m.

According to the Heron's formula, the area of a triangle is

where,

In triangle ACD,

Using Heron's formula, the area of the triangle ACD, we get

Now, the area of the quadrilateral is the sum of area of the triangle ABC and triangle ACD.

Therefore, the area of the quadrilateral ABCD is 306 square meter.

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step-by-step explanation:

step-by-step explanation:

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