Question

a kite is made up of two isosceles triangles, kit and ket, with the lengths shown. the top triangle of the kite, δkit, is made from approximately 17 square inches of material. how much material is used for the entire kite, quadrilateral kite? round to the nearest square inch. 31 square inches 34 square inches 48 square inches 62 square inches herons formula: area = \sqrt{s(s - a)(s - b)(s - c)}

Explanation:

Step1: Calculate semi - perimeter of $\triangle KET$

For $\triangle KET$ with $a = 8$, $b = 8$, $c = 10$, the semi - perimeter $s=\frac{8 + 8+10}{2}=\frac{26}{2}=13$ inches.

Step2: Calculate area of $\triangle KET$ using Heron's formula

$A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{13(13 - 8)(13 - 8)(13 - 10)}=\sqrt{13\times5\times5\times3}=\sqrt{975}\approx31.22$ square inches.

Step3: Calculate area of the kite

The area of $\triangle KIT$ is approximately 17 square inches. The area of the kite (quadrilateral $KITE$) is $A_{kite}=A_{\triangle KIT}+A_{\triangle KET}\approx17 + 31.22=48.22\approx48$ square inches.

Answer:

48 square inches