Question

PQRS is a rectangle and AQRB is a || gm, SR = 9 cm, PS = 12 cm

Area of ΔCQR =

Options

• 108 cm²

• 72 cm²

• 54 cm²

• 42 cm²

Answer 1

54 cm²

Explanation:

Given:

• PQRS is a rectangle.
• AQRB is a parallelogram.
• SR = 9 cm
• PS = 12 cm

To find: Area of ΔCQR

Since PQRS is a rectangle, PS and SR are perpendicular sides. PS = 12 cm, SR = 9 cm.

Length PR (diagonal) can be found using the Pythagoras theorem because triangle PSR is a right triangle:

PR = `sqrt(PS^2 + SR^2)`

= `sqrt(12^2 + 9^2)`

= `sqrt(144 + 81)`

= `sqrt225`

= 15 cm

Area of triangle CQR lies within the rectangle and parallelogram figures. By the given figure and properties, the area calculation involves base and height found by SR and PS.

The area of triangle CQR is given by

`1/2` × base × height

`1/2 xx SR xx PS`

`1/2 xx 9 xx 12`

54 cm²