Question

In the Kite ABCD, AB = 52‾√52 mm AP= 5 mm, PD = 7 mm, find the area to the nearest mm2.

Answer 1

$\begin{equation*} 140\text{ mm}^2 \end{equation*}$

Explanation

Step 1

the area of a kite is given by:

The area of a kite is half the product of the lengths of its diagonals

$Area=x*y$

Step 1

given the rigth triangle

so, we can find the x and y values

hence

a)x

$\begin{gathered} \frac{x}{2}=\text{ 5} \\ to\text{ solve for x, multiply both sides by 2} \\ \frac{x}{2}*2=5*2 \\ x=10 \end{gathered}$

b) y

$\begin{gathered} \frac{y}{2}=7 \\ to\text{ solve for y, multiply both sides by 2} \\ \frac{y}{2}*2=7*2 \\ y=14 \end{gathered}$

so

x=10

y=14

Step 2

finally, replace in the formula to find the area

$\begin{gathered} Area=xy \\ area=10\text{ mm *14 mm} \\ area=140\text{ mm}^2 \end{gathered}$

therefore, the answer is

$\begin{equation*} 140\text{ mm}^2 \end{equation*}$

I hope this helps you