A baker is baking a giant cookie in the shape of an equilateral triangle. What is the area of the cookie if the base is 17 inches and the height is 10 inches?
If those dimensions are correct, it is not an equilateral triangle.
To find the area of an equilateral triangle, you can use the formula:
Area = (base * height) / 2
Given that the base is 17 inches and the height is 10 inches, we can substitute these values into the formula.
Area = (17 * 10) / 2
= 170 / 2
= 85
So, the area of the giant cookie, in the shape of an equilateral triangle, is 85 square inches.
To find the area of an equilateral triangle, you need to know the length of one side. However, in this case, we are given the base and the height of the triangle.
Since the cookie being baked is in the shape of an equilateral triangle, we know that all three sides are of equal length.
To find the length of each side, we can use the Pythagorean theorem.
The height of the equilateral triangle represents the altitude, or a perpendicular distance from the base to the opposite vertex. In our case, the height is given as 10 inches. Now, we can divide the triangle into two right triangles.
Using the Pythagorean theorem, we can calculate the length of the sides of each right triangle. The hypotenuse of the right triangle is the side of the equilateral triangle and the base of the right triangle is half the length of the base of the equilateral triangle.
In our case, the base of the right triangle is 17/2 inches (half of the base of the equilateral triangle). The hypotenuse would be the length of each side of the equilateral triangle, which is the unknown we are trying to find.
Applying the Pythagorean theorem:
(17/2)^2 + 10^2 = c^2
289/4 + 100 = c^2
289 + 400 = c^2
689 = c^2
Taking the square root on both sides gives us the length of each side, which is approximately 26.26 inches.
Now that we know the length of each side, we can calculate the area of the equilateral triangle using the formula:
Area = (side length ^ 2 * √3) / 4
In our case, the side length is approximately 26.26 inches.
Plugging this value into the formula:
Area = (26.26^2 * √3) / 4
= (689.2276 * √3) / 4
≈ 376.9902 square inches
Therefore, the area of the giant cookie is approximately 376.9902 square inches.