Question : A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm. The area of the parallelogram is:
Option 1: 42 cm2
Option 2: 60 cm2
Option 3: 84 cm2
Option 4: 96 cm2
Correct Answer: 84 cm 2
Solution :
Given: A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm.
Let ABCD be the parallelogram.
The diagonal of a parallelogram divides it into two equal triangles.
The half perimeter of one of the triangles,
Area of triangle by heron's formula =
So, the area of one of the triangles is:
=
=
= 42 cm
2
So, Area of the parallelogram = 2 × Area of one of its triangles = (2 × 42) cm
2
= 84 cm
2
Hence, the correct answer is 84 cm
2
.
