Name: Figures on the Same Base
Uploaded: 2019-07-19
Duration: 6 min 34 s
Description: Two figures are said to be on one base and between the same parallels if they have a common side as the base and certain vertices lie on the line parallel to...

Question

Find the area of parallelogram $A B C D$ , if $AD = 15 cm$ and $P$ is a point on $B C$ such that $AP = 9 cm$ . Also find the area of parallelogram $A B Q R$ , where $Q$ and $R$ are the points on $C D$ produced.

Accepted Answer

In $△ A P D$ ,

Using Pythagoras theorem

$A D^{2} = A P^{2} + P D^{2}$

$\Rightarrow 15^{2} = 9^{2} + P D^{2}$

$\Rightarrow P D^{2} = 225 - 81 = 144$

$\Rightarrow PD = 12 cm$

We know that,

Area of a triangle $= \frac{1}{2} \times base \times height$

It is given that, $PD = 15 cm, AP = 9 cm$

$∴$ Area of $△ A P D = \frac{1}{2} \times P D \times A P$

$= \frac{1}{2} \times 12 \times 9 = \frac{108}{2} = 59 {cm}^{2}$

Since $A B Q R$ and $Q$ are drawn on the same base $A D$ and between the same parallel lines $A D & B C$ . So, the area of the triangle is half of the area of the parallelogram.

$\Rightarrow ar (∥ gm ABCD) = 2 \times 59 = 108 {cm}^{2}$

Parallelograms on the same base and between the same parallels are equal in area.

Since, $∥ gm ABQR$ and $∥ gm ABCD$ are on same base $A B$ and between same parallels $AB & CR$ .

$∴ ar (∥ gm ABQR) = ar (∥ gm ABCD) = 108 {cm}^{2}$

Find the area of parallelogram $A B C D$ , if $AD = 15 cm$ and $P$ is a point on $B C$ such that $AP = 9 cm$ . Also find the area of parallelogram $A B Q R$ , where $Q$ and $R$ are the points on $C D$ produced.

Important Questions on Theorems on Area

Learn and Prepare for any exam you want !

Find the area of parallelogram ABCD, if AD=15 cm and P is a point on BC such that AP=9 cm. Also find the area of parallelogram ABQR, where Q and R are the points on CD produced.

Important Questions on Theorems on Area

Learn and Prepare for any exam you want !

Find the area of parallelogram $A B C D$ , if $AD = 15 cm$ and $P$ is a point on $B C$ such that $AP = 9 cm$ . Also find the area of parallelogram $A B Q R$ , where $Q$ and $R$ are the points on $C D$ produced.