SOLUTION: A kite is formed by an equilateral triangle with sides 6 cm and an isosceles triangle with legs 5 cm. Find the area of the kite.

Question 870442: A kite is formed by an equilateral triangle with sides 6 cm and an isosceles triangle with legs 5 cm. Find the area of the kite.

Answer by ben720(159) (Show Source): You can put this solution on YOUR website!
Firstly, find the area of the equilateral triangle by using

.
We already know the base

The height of an equilateral triangle is times one of the sides.

Substitute h

The area of the equilateral triangle is

Finding the area of the isosceles triangle will be harder. Firstly, we know two sides are 5cm. The third side has to be the same as one of the equilateral triangle's sides, because the isosceles and equilateral are connected. So, the other isosceles triangle side is 6cm.
Next, we need to find the height, relative to the 6cm side. Use the Pythagorean Theorem to do so:
Substitute

The height of the isosceles triangle is 4, so the area is 24. The areas of the triangles added together is
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