Question : Let A, B, and C be the mid-points of sides PQ, QR, and PR, respectively, of PQR. If the area of $\triangle$ PQR is 32 cm2, then find the area of $\triangle$ ABC.
Option 1: 24 cm2
Option 2: 16 cm2
Option 3: 32 cm2
Option 4: 8 cm2
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Correct Answer: 8 cm 2
Solution :
Given: Let A, B, and C be the mid-points of sides PQ, QR, and PR, respectively of $\triangle$PQR, the area of $\triangle$PQR is 32 cm
2
.
We know,
Area of $\triangle$ABC = $\frac{1}{4}$ × (Area of $\triangle$PQR)
So, the area of $\triangle$ ABC
= $\frac{1}{4}$ × 32
= 8 cm
2
Hence, the correct answer is 8 cm
2
.
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