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.