Question

$ABCD$ is a parallelogram, $p$ is any point on $CD$. If $ar\left(DPA\right)=15c{m}^2$ and $ar\left(APC\right)=20c{m}^2$ then $ar\left(APB\right)=$

• A. $15c{m}^2$
• B. $20c{m}^2$
• C. $35c{m}^2$
• D. $30c{m}^2$

Answer 1

The correct option is C $35c{m}^2$

area $\left(DPA\right)=15c{m}^2$

area $\left(APC\right)=20c{m}^2$

area $\left(APB\right)=?$

area of $△ACD=(15+20)c{m}^2$

$=35c{m}^2$

Now in a parallelogram opp sides are equal.

$\therefore CD=AB$

also $AB\parallel CD$

Now, we know,

triangles having same base and lie with same $\parallel$ have same area

area of $△ABP=$ area of $△ACD$

$=35cm$.