Problem:
The area of triangle is square inches. Points and are midpoints of congruent segments and . Altitude bisects . The area (in square inches) of the shaded region is
Answer Choices:
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B.
C.
D.
E.
Solution:
Segments and are drawn perpendicular to . Segments , and divide into four congruent triangles. Vertical line segments and divide each of these in half. Three of the eight small triangles are shaded, or of . The shaded area is .
Segments and divide into four congruent triangles, so the area of is one-fourth the area of . That makes the area of trapezoid three-fourths the area of . The shaded area is one-half the area of trapezoid , or three-eighths the area of , and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions