Q35: Midpoints of the sides of the square

October 15, 2026

2018 Test B Math · Question 35 of 57

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$\dpi{100} \dpi{100}R, S, \textup{and} T \textup{are midpoints of the sides of square} \: MNPQ,\\ \textup{as shown above.What is the sum of the areas of the shaded triangles?}$

A9 sq cm
B12 sq cm
C18 sq cm
D36 sq cm

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Correct answer: A

The length of one side of the square is 6 cm. Since $R$ , $S$ , and $T$ are midpoints, then $TM$ , $MR$ , $RN$ , and $NS$ are all equal to 3 cm. Triangles $TMR$ and $RNS$ are both right triangles, so the area of one of the triangles is

$(frac{1}{2})(3)(3)=frac{9}{2}$

The triangles are congruent, so the sum of the areas is

$frac{9}{2}+frac{9}{2}=frac{18}{2}=9$