Chapter 11.4, Problem 5PSB

a

To determine

To calculate: The area of rhombus with side $25$ and diagonal $14$ .

Answer to Problem 5PSB

Area of rhombus is $336$ square units.

Explanation of Solution

Given information :

One side of rhombus is $25$ and one diagonal is $14$ .

Formula used : Area of rhombus = $\frac{1}{2}\times d_1\times d_2$ (where $d_1$ and $d_2$ are diagonals of the rhombus) and Pythagoras Theorem = ${(Hypotenuse)}^2={(Perpendicular)}^2+{(Base)}^2$

Calculation: Let ABCD be the rhombus and AC and BD be the diagonals of the rhombus.

  $\Rightarrow BD=14$ and $CD=15$

Now, In $\Delta COD$ , $OD=7$ (diagonals of rhombus bisect each other in two equal halves), $CD=25$ and $\angle COD=90°$ .

  $\begin{array}{l}$ \Rightarrow {(25)}^2={(7)}^2+{(OC)}^2$\Rightarrow 625=49+O{C}^2\\ \Rightarrow O{C}^2=625-49\\ \Rightarrow O{C}^2=576\\ \Rightarrow OC=\sqrt{576}\\ \Rightarrow OC=24\end{array}$

  $\therefore$ By Pythagoras theorem, ${(CD)}^2={(OD)}^2+{(OC)}^2$

  

Now, $AC=2(OC)$ (diagonals of rhombus bisect each other in two equal halves)

  $\Rightarrow AC=2(24)=48$

  $\therefore$ Diagonals of rhombus are $14$ and $48$ .

Area of rhombus = $\frac{1}{2}\times d_1\times d_2$

  $\begin{array}{l}\Rightarrow \frac{1}{2}\times 14\times 48\\ \Rightarrow 7\times 48\\ \Rightarrow 336\end{array}$

b

To determine

To calculate: The area of rhombus with side $25$ and height $20$ .

Answer to Problem 5PSB

Area of rhombus is $500$ square units.

Explanation of Solution

Given information : One side of rhombus is $25$ and Height is $20$ .

Formula used : Area of rhombus = $b\times h$ (where b is base of the rhombus)

Calculation: Area of rhombus = $b\times h$

  $\begin{array}{l}\Rightarrow 25\times 20\\ \Rightarrow 500\end{array}$