PQST is a rectangle. The area of triangle PQR is 18m square and the area of triangle PTR is 32m square. What is the area of triangle TRS.

Question

P Q

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Answer 1

Let a = length of PQ.

Let b = length of PT.

Then, the area of rectangle PQST = ab.

The area of triangle PQR is 18 m².

The area of triangle PTR is 32 m². This means that

(1/2)ab = 32

or

ab = 64 m², which is the area of rectangle PQST.

From the figure,

Area of triangle TRS = Area of rectangle PQST - Area of triangle PQR - Area of triangle PTR.

That is,

Area of triangle TRS = 64 - 18 - 32 = 14 m².

Answer: 14 m².