Question
Find the area of an isosceles triangle with a base of 15 and legs that are 10 each.
Answers
GPT 3.5
To find the area of an isosceles triangle, we use the formula:
Area = (base * height) / 2
Since our triangle is isosceles, we can draw a line down from the vertex opposite the base to the midpoint of the base, creating two right triangles with legs of 5 and a hypotenuse of 10 (half of the base). We can use the Pythagorean theorem to find the height of the triangle:
c^2 = a^2 + b^2
10^2 = 5^2 + h^2
100 = 25 + h^2
75 = h^2
h = √75 = 5√3
Now that we have the height of the triangle, we can find the area:
Area = (15 * 5√3) / 2
Area = 75√3 / 2
Area = 37.5√3
Therefore, the area of the isosceles triangle is 37.5√3 square units.
Area = (base * height) / 2
Since our triangle is isosceles, we can draw a line down from the vertex opposite the base to the midpoint of the base, creating two right triangles with legs of 5 and a hypotenuse of 10 (half of the base). We can use the Pythagorean theorem to find the height of the triangle:
c^2 = a^2 + b^2
10^2 = 5^2 + h^2
100 = 25 + h^2
75 = h^2
h = √75 = 5√3
Now that we have the height of the triangle, we can find the area:
Area = (15 * 5√3) / 2
Area = 75√3 / 2
Area = 37.5√3
Therefore, the area of the isosceles triangle is 37.5√3 square units.