In△PQRthe midpoints ofPQandPRareOandS respectively. If the area of OQRSis 54cm2 , find the area of △PQR .
Question
In△PQRthe midpoints ofPQandPRareOandS respectively. If the area of OQRSis 54cm2 , find the area of △PQR .
Solution
The area of a triangle formed by joining the midpoints of the sides of a given triangle is 1/4 of the area of the given triangle.
In this case, OQRS is a parallelogram formed by joining the midpoints of the sides of triangle PQR. Since the diagonals of a parallelogram bisect each other, triangle ORS is half the area of parallelogram OQRS.
So, the area of triangle ORS is 54/2 = 27 cm².
Since triangle ORS is 1/4 the area of triangle PQR, the area of triangle PQR is 4 times the area of triangle ORS.
So, the area of triangle PQR is 4 * 27 = 108 cm².
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