Question - Calculating Perimeter and Area of a Trapezoid
Solution:
The shape in the image appears to be a trapezoid. To find the perimeter of the trapezoid, you would add up the lengths of all four sides. Two sides are given as 4 ft and 18 ft. However, the other two sides are not perpendicular to each other, so you can't directly add the given 14.6 ft to the perimeter since 14.6 ft is the slant height, not the height of the trapezoid.You must calculate the lengths of the other two sides. The vertical height of the trapezoid (from the shorter base to the longer base) is not given, but we can see that it forms a right-angled triangle along with the 14.6-foot side and the part of the 18-foot base that extends beyond the 4-foot wide top base. To find the length of this portion of the bottom base, we subtract the upper base length from the full bottom base length:18 ft - 4 ft = 14 ftNow, using the Pythagorean theorem for the right triangle where the slant side (hypotenuse) is 14.6 feet, the base is 14 feet, and we need to find the height (h), we have:h^2 + 14^2 = 14.6^2h^2 + 196 = 213.16h^2 = 213.16 - 196h^2 = 17.16h = √17.16h ≈ 4.14 ftNow we can find the perimeter of the trapezoid by adding up all four sides:Perimeter = 4 ft + 4 ft + 18 ft + 14.6 ftPerimeter = 40.6 ftThis matches one of the given options so the perimeter is 40.6 feet.For the area of a trapezoid, the formula is:Area = 1/2 * (sum of parallel sides) * heightArea = 1/2 * (4 ft + 18 ft) * 4.14 ftArea = 1/2 * 22 ft * 4.14 ftArea = 11 ft * 4.14 ftArea ≈ 45.54 sq ftSo the area of the trapezoid is approximately 45.54 square feet.
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