SOLUTION: (19) For triangle PQR, V and S are the midpoints of sides PQ and QR respectively. VQST is a rectangle with VQ = 6.25 and QS = 2.56. Find the area of the shaded region. Link to g

Question 1209483: (19) For triangle PQR, V and S are the midpoints of sides PQ and QR respectively. VQST is a rectangle with VQ = 6.25 and QS = 2.56. Find the area of the shaded region.
Link to graph: https://ibb.co/ZhtYbwH
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

VQST is a rectangle, so triangles PQR, PVT, and TSR are all similar right triangles.

Furthermore, since V and S are the midpoints of PQ and QR respectively, triangles PVT and TSR are congruent.

So the ratio of similarity between triangle PQR and each of the other two triangles is 2:1. That means the ratio of the areas of triangles PQR and PVT is 2^2:1^2 = 4:1.

So each of triangles PVT and TSR has an area 1/4 the area of triangle PQR. And then, since the area of the shaded region is the sum of the areas of triangles PVT and TSR, the area of the shaded region is 2/4 = 1/2 of the area of triangle PQR. But the area of VQST is also 1/2 the area of triangle PQR, so the area of the shaded region is equal to the area of VQST.

And the area of rectangle VQST is length times width = VQ*QS = 6.25*2.56 = 16.

ANSWER: 16

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