A landscape architect is designing a courtyard in the shape of a right trapezoid. The parallel sides of the courtyard have lengths of yards and yards. The side perpendicular to the parallel sides has a length of yards. A straight path is built from the midpoint of the longer parallel side to the vertex of the shorter parallel side that is adjacent to the perpendicular side, dividing the courtyard into two regions. What is the area, in square yards, of the smaller region?
Answer: 150 square yards
Answer
The area of the smaller region is 150 square yards.
The straight path divides the right trapezoid into two regions: a right triangle and a quadrilateral. The right triangle has a vertical leg of 15 yards (the height of the trapezoid) and a horizontal leg of 20 yards (half of the longer parallel side of 40 yards). The area of this right triangle is 0.5 * 20 * 15 = 150 square yards. The total area of the trapezoid is 0.5 * (24 + 40) * 15 = 480 square yards, making the area of the quadrilateral region 480 - 150 = 330 square yards. Comparing the two regions, the smaller region has an area of 150 square yards.
Step-by-Step Solution
Key Concept
Area of composite shapes and trapezoids