5. Find the area of an isosceles triangle with a base of 15 and legs that are 10 each. (Type the answer without units, and round to the nearest tenth if your answer is not a whole number.)(1 point)
The area of an isosceles triangle can be calculated using the formula:
Area = 0.5 * base * height
In an isosceles triangle, the height is the altitude from the vertex to the base, which bisects the base and forms two right triangles. The altitude can be found using the Pythagorean theorem:
10^2 = x^2 - (15/2)^2
100 = x^2 - 112.5
x^2 = 212.5
x ≈ 14.6
Therefore, the height of the triangle is approximately 14.6.
Plugging the values into the area formula:
Area = 0.5 * 15 * 14.6
Area = 108.75
The area of the isosceles triangle is approximately 108.8.