smc

Question

In rhombus ABCD, point P lies on segment AD so that BP AD, AP = 3, and PD = 2. What is the area of ABCD? (Note: The figure is not drawn to scale.) FIGURE

Accepted Answer

FIGURE Figure redrawn to scale. AD = AP + PD = 3 + 2 = 5. ABCD is a rhombus, so AB = AD = 5. APB is a 3-4-5 right triangle, hence BP = 4. The area of the rhombus is base times height: bh = (AD)(BP) = 5 4 = 20.