Chapter 11, Problem 18RP

To determine

To calculate:Thearea of parallelogram ABCD .

Answer to Problem 18RP

The area of parallelogram ABCDis $21\sqrt{2}$ .

Explanation of Solution

Given information:

In a parallelogram ABCD ,

Side AB = 7,

Side AD = 6.

Angle D = ${45}^{\circ }$

Formula used:

Side opposite to ${45}^{\circ }$ angle = $\frac{1}{\sqrt{2}}\times hypotenuse$

Area of parallelogram: $A=b\times h$

b =base of parallelogram

h= height of parallelogram

Calculation:

  

Draw the altitude AE .

ΔADE is ${45}^{\circ }{45}^{\circ }{90}^{\circ }\Delta$

Side opposite to ${45}^{\circ }$ angle= $\frac{1}{\sqrt{2}}\times hypotenuse=\frac{1}{\sqrt{2}}\times 6=\frac{6}{\sqrt{2}}=3\sqrt{2}$

AD = 6 and AE $=3\sqrt{2}$

DC = AB =7

Area of parallelogram:

  $\begin{array}{l}A(▱ABCD)=DC\times AE\\ A(▱ABCD)=7\times 3\sqrt{2}\\ A(▱ABCD)=21\sqrt{2}\end{array}$