Question

a kite is made up of two isosceles triangles, kit and ket, with the lengths shown. the top triangle of the kite, △kit, 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. herons formula area = \sqrt{s(s - a)(s - b)(s - c)} o 31 square inches o 34 square inches o 48 square inches o 62 square inches

Explanation:

Step1: Recognize the kite structure

The kite is composed of two isosceles - triangles $\triangle KIT$ and $\triangle KET$. Given the area of $\triangle KIT$ is approximately 17 square inches.

Step2: Use the property of kites

The two isosceles - triangles $\triangle KIT$ and $\triangle KET$ are congruent (by the symmetry of a kite). So the area of $\triangle KET$ is the same as the area of $\triangle KIT$.

Step3: Calculate the total area

The total area of the kite (quadrilateral $KITE$) is the sum of the areas of the two triangles. Let $A_1$ be the area of $\triangle KIT$ and $A_2$ be the area of $\triangle KET$. Since $A_1 = A_2=17$ square inches, the total area $A = A_1 + A_2$.
$A=17 + 17=34$ square inches.

Answer:

34 square inches