Trapezoid ABCD has height 4, BC=5, and AD and BC are perpendicular. Find the area of the trapezoid.
To find the area of the trapezoid, you can use the formula:
Area = (sum of the lengths of the parallel sides / 2) * height
In this case, the parallel sides of the trapezoid are BC and AD, and the height is given as 4. The length BC is given as 5, but the length of AD is not provided.
However, since AD and BC are perpendicular, we can use the Pythagorean theorem to find the length of AD.
The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
In this case, a = BC = 5 and b = height = 4. We can solve for c, which will give us the length of AD.
c^2 = 5^2 + 4^2
c^2 = 25 + 16
c^2 = 41
Taking the square root of both sides, we get:
c ≈ √41
Now that we have the lengths of both BC and AD, we can substitute these values into the formula for the area of a trapezoid:
Area = (BC + AD) / 2 * height
Area = (5 + √41) / 2 * 4
Area ≈ (5 + √41) / 2 * 4
Now, you can use a calculator to find the approximate value of the area.