A trapezoid has two sides the length of 8 in, the top width being 10 in and the bottom width being 12 in. Find the area of the trapezoid.
To find the area of a trapezoid, you can use the formula:
Area = 1/2 * (b1 + b2) * h
Where b1 and b2 are the lengths of the two bases and h is the height of the trapezoid.
In this case, b1 = 10 in, b2 = 12 in, and h is the perpendicular distance between the two bases. We can find h by using the Pythagorean theorem:
h^2 = c^2 - a^2
h^2 = 8^2 - ((12-10)/2)^2
h^2 = 64 - 2^2
h^2 = 64 - 4
h^2 = 60
h = sqrt(60)
h ≈ 7.746 in
Now we can plug in the values into the formula:
Area = 1/2 * (10 + 12) * 7.746
Area = 1/2 * 22 * 7.746
Area = 11 * 7.746
Area ≈ 85.206 square inches
So, the area of the trapezoid is approximately 85.206 square inches.