Question

ABCD is a parallelogram and 'Q' is a point on AB. If area of CED is 10 cm${}^2$ then find Ar (QAD) + Ar (QBC).

• A. 10 cm${}^2$
• B. 5 cm${}^2$
• C. 15 cm${}^2$
• D. None of these

Answer 1

The correct option is A 10 cm${}^2$

Given, area of CED is 10 cm${}^2$

Form the above figure :
Area of ABCD = Area of QCD + Area of QAD + Area of QBC
$\because$ If a triangle and a parallelogram are on the same base and between same parallel lines, then $\text{Area of triangle}=\frac{1}{2}\times \text{Area of parallelogram}$
$\therefore$ Area of ABCD = $2\times$ Area of QCD
$\Rightarrow 2\times$ Area of QCD = Area of QCD + Area of QAD + Area of QBC
$\Rightarrow \text{Area of QAD + Area of QBC = Area of QCD}$
$\Rightarrow {\text{Area of QAD + Area of QBC = 10 cm}}^2$