Question

In the given figure, PQRS is a rectangle of area $35c{m}^2$. Find the area of $\Delta EFT.$

• A. $35c{m}^2$
• B. $70c{m}^2$
• C. $17.5c{m}^2$
• D. $60c{m}^2$

Answer 1

The correct option is C $17.5c{m}^2$

Paralellograms PQRS and EFRS lie on the same base SR and between the same parallel lines ST and PF.

We know that, Parallelograms on the same base and between the same parallels are equal in area.

Implies, Area rectangle PQRS = area ||gm EFRS $=35c{m}^2$

In $\Delta$ EFT and ||gm EFRS,
EF is common base and lies between parallel lines EF and ST

$\because$ Area of triangle is equal to half the area of the ||gm if they have the same base and are between the same parallels

$\therefore$ area $\Delta EFT=\frac{1}{2}$ area ||gm EFRS

$=\frac{1}{2}\times 35$

$=17.5c{m}^2$