Question

State True or False In the given fig. $ABP$ is a straight line $BD\parallel PC$, then the quadrilateral ABCD is equal in area to $\Delta APD$

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ $ABCD$ is quadrilateral and $BD\parallel PC.$

In $△BCD$ and $△BPD$ are lie on the same base $BD$ and between the same parallel line $BD$ and $CP$.

$\therefore$ $ar\left(△BCD\right)=ar\left(△BPD\right)$

Adding $ar\left(△ABD\right)$ on both sides we get,

$\Rightarrow$ $ar\left(△ABD\right)+ar\left(△BCD\right)=ar\left(△ABD\right)+ar\left(△BPD\right)$

$\Rightarrow$ $ar\left(\square ABCD\right)=ar\left(△APD\right)$

$\therefore$ Given statement is true.