The amount of material needed to cover one side of the kite is 160 square inches
Start by calculating lengths AE and CE using Pythagoras theorem
Length AE
[tex]13^2 = 5^2 + AE^2[/tex]
[tex]169 = 25 + AE^2[/tex]
Collect like terms
[tex]AE^2 =169 - 25[/tex]
[tex]AE^2 =144[/tex]
Take the square roots of both sides
[tex]AE =12[/tex]
Length CE
[tex](\sqrt {425})^2 = 5^2 + CE^2[/tex]
[tex]425 = 25 + CE^2[/tex]
Collect like terms
[tex]CE^2 = 425 - 25[/tex]
[tex]CE^2 = 400[/tex]
Take the square roots of both sides
[tex]CE = 20[/tex]
The area of the kite is then calculated as:
[tex]Area = \frac{1}{2} \times[ AE \times (2DE) + CE \times (2DE)][/tex]
[tex]Area = \frac{1}{2} \times[ 12 \times (2 \times 5) + 20 \times (2 \times 5)][/tex]
[tex]Area = \frac{1}{2} \times[ 320][/tex]
[tex]Area = 160[/tex]
Hence, the area of the kite is 160 square inches
Read more about areas at:
https://brainly.com/question/2292872
