In the given figure, PQRS is a quadrilateral. If QR = 18 cm and PS = 9 cm, then what is the area (in cm2) of two such quadrilateral PQRS?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 135√3/2.
Given: QR = 18 cm and PS = 9 cm
In triangle APS:
Tan30 = AS/PS
AS = 9/√3 = 3√3 cm
So,
Area of triangle APS = 1/2 × PS × AS
= 1/2 × 9 × 3√3 = 27√3/2 cm2
In triangle RAQ:
All angles are 60° so it is an equilateral triangle.
AQ = AR = QR = 18 cm
So,
Area of triangle RAQ = √3/4 × (18)2 = 81√3 cm2
∴ Area of quadrilateral PQRS = 81√3 - 27√3/2 = 135√3/2 cm2
The area of two such quadrilateral = 2 × 135√3/2 = 135√3 cm2