Question

ABCD is a parallelogram. P is any point on CD. If ar($△$DPA) = 35 $c{m}^2$ and ar($△$APC) = 15 $c{m}^2$, then area of ($△$APB) is equal to

• A. 15 cm²
• B. 35 cm²
• C. 50 cm²
• D. 70 cm²

Answer 1

Answer: (A), (C)

The correct options are
A

15 cm²

C

50 cm²

$Area\left(\Delta ACD\right)=Area\left(\Delta APD\right)+Area\left(\Delta ACP\right)=50c{m}^2\text{Now,}ABCD\text{is a parallelogram.}\therefore DC=AB.\therefore \Delta APB\text{and}\Delta ADC\text{have equal bases}\left(AB\text{and}DC\right)\text{and they are between same parallels}\left(AB\text{and}DC\right)\text{Hence,}Area\left(\Delta APB\right)=Area\left(\Delta ACD\right)=50c{m}^2$