Question

PQRS is a parallelogram with PS = 4 cm and AR $\parallel$ PB. If Area of triangle APS = 48 $c{m}^2$, find the height of triangle QRB. [2 MARKS]

Answer 1

Concept : 1 Mark
Calculation : 1 Mark

PS = QR = Base of $△$QRB = 4 cm

Parallelogram PQRS and triangle APS are on same base PS and between same parallels .

ar($△$APS)= $\frac{1}{2}$ ar(PQRS)

Also, Parallelogram PQRS and triangle QRB are on same base QR and between same parallels QR and PS .

ar($△$QRB)= $\frac{1}{2}$ ar(PQRS)

So, ar($△$APS) = ar($△$QRB) = 48 $c{m}^2$
ar($△$QRB) = $\frac{1}{2}$× QR × required height

$\Rightarrow$ 48 = $\frac{1}{2}$ × 4 × height
$\Rightarrow$ height = 24 $cm$