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.

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Firstly, find the area of the equilateral triangle by using
A=1%2F2%2Ab%2Ah
.
We already know the base
A=1%2F2%2A6%2Ah
The height of an equilateral triangle is sqrt%283%29%2F2 times one of the sides.
sqrt%283%29%2As%2F2=3sqrt%283%29
Substitute h
A=1%2F2%2A6%2A3sqrt%283%29
A=9sqrt%283%29
The area of the equilateral triangle is 9sqrt%283%29

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: c%5E2=a%5E2%2Bb%5E2
Substitute
5%5E2=3%5E2%2Bb%5E2
25=9%2Bb%5E2
16=b%5E2
4=b
The height of the isosceles triangle is 4, so the area is 24. The areas of the triangles added together is 24%2B9sqrt%283%29