Question

The area of triangle XY Z is 8 square inches. Points A and

B are midpoints of congruent segments XY and XZ. Altitude

XC bisects Y Z. What is the area (in square inches) of the

shaded region?​

Answer 1

Answer:

The shaded region is a right trapezoid. Assume WLOG that $YZ=8$. Then because the area of $\triangle XYZ$ is equal to 8, the height of the triangle $XC=2$. Because the line $AB$ is a midsegment, the top base of the triangle is $\frac12 AB = \frac14 YZ = 2$. Also, $AB$ divides $XC$ in two, so the height of the trapezoid is $\frac12 (2) = 1$. The bottom base is $\frac12 YZ = 4$. The area of the shaded region is $\frac12 (2+4)(1) = \boxed{\text{(D)}\ 3}$.