Question

If a parallelogram having area $48{\text{cm}}^2$ and height 6 cm is transformed into a triangle with the same base and area as that of the parallelogram, then what is the height of the triangle?

• A. 9 cm
• B. 12 cm
• C. 18 cm
• D. 24 cm

Answer 1

The correct option is B 12 cm

Area of a parallelogram = base $\times$ height
$⟹48=\text{base}\times 6$
$⟹\text{base}=\frac{48}{6}=8cm$

Given that the base and area of the parallelogram is same as that of the triangle ,
$⟹$ Area of triangle = 48 = $\frac{1}{2}\times \text{base}\times \text{height}$
$⟹48=\frac{1}{2}\times 8\times \text{height}$
$⟹$Height of the triangle =$\frac{48\times 2}{8}=12cm$