What is the area of an equilateral triangle with sides of 10 inches and height of 7 inches? Can you please check my answer and my reasoning?

A. 44 sq. in.
B. 20 sq. in.
C. 70 sq. in.
D. 35 sq. in.

I picked D, because I took 10x7=70and divided that by 2, which equals 35 sq. in. for a triangle area. If I am wrong please let me know.

5 answers

Right.

D looks good

but of course, an equilateral triangle with sides of 10, has a height of 8.66

So, the triangle is isosceles, but not equilateral.

Thanks

Thanks to both of you

To find the area of an equilateral triangle, you can use the formula:

Area = (s^2 * √3) / 4

Where "s" is the length of one side of the triangle.

In this case, you have an equilateral triangle with sides of 10 inches. Let's substitute the value of "s" into the formula:

Area = (10^2 * √3) / 4

Area = (100 * √3) / 4

Area ≈ 43.301 sq. in. (rounded to three decimal places)

Based on your calculations, you used the height of 7 inches instead of the side length to calculate the area. This would be correct if you were dealing with a right-angled triangle, but not for an equilateral triangle.

Therefore, your answer of D (35 sq. in.) is incorrect. The correct answer is closest to A (44 sq. in.).