Chapter 11.2, Problem 31PPS

To determine

To calculate: The area of given figure.

Answer to Problem 31PPS

  $\begin{array}{l}\text{Area of given figure(rhombus) = }178.5{\text{ m}}^2\\ =1920.4\text{ square feet}\end{array}$

Explanation of Solution

Given information: Diagonals of given figure (rhombus) are 17 m and 21 m.

Formula used: Area of rhombus using diagonals is given by

  $\text{Area of rhombus = }\frac{1}{2}\times d_1\times d_2$ ……(1)

where, $d_1\&d_2$ are diagonals of rhombus.

Calculation: Here, $\begin{array}{l}{d}_1=17\text{ m}\\ d_2=21\text{ m}\end{array}$

Putting the value of $d_1\&d_2$ in (1),

  $\begin{array}{l}\text{Area of given figure(rhombus) = }\frac{1}{2}\times d_1\times d_2\\ =\frac{1}{2}\times 17\times 21\\ =\frac{357}{2}\\ =178.5{\text{ m}}^2\end{array}$

We know, $1\text{ m }=3.28\text{ feet}$

  $\begin{array}{l}\text{Area of given figure(rhombus) = }178.5{\text{ m}}^2\\ =178.5\times 3.28\times 3.28\text{ square feet}\\ =1920.3744\text{ square feet}\\ =1920.4\text{ square feet}\end{array}$

Thus, $\begin{array}{l}\text{Area of given figure(rhombus) = }178.5{\text{ m}}^2\\ =1920.4\text{ square feet}\end{array}$