A cyclic quadrilateral has sides 5, 5, 12, 12 units. Find its area. Class 9

A cyclic quadrilateral has sides 5, 5, 12, 12 units. Find its area. Class 9

Question 1.

A cyclic quadrilateral has sides 5, 5, 12, 12 units. Find its area. Class 9

Solution:

ABCD is cyclic quadrilateral.

AB = AD = 5 units and BC = CD = 12 units

Since the sum of two opposite angles of a cyclic quadrilateral is 180°

∠B + ∠D = 180°

∴ ∠B = ∠D = 90°

AC divides quadrilateral ABCD into two right-angled triangles.

A(ABC) = A(∆ADC)

= $\frac{1}{2}$ × 5 × 12

= 30 sq. units

∵ A(☐ABCD) = A(∆ABC) + A( ∆ADC)

= 30 + 30

= 60 units

∴ Area of cyclic quadrilateral is 60 sQuestion units.