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There are two congruent triangles each with area 198 cm2. Triangle DEF is placed over triangle ABC in such a way that the centroid of both the triangles coincide with each other and AB || DE as shown in the figure forming a star. What is the area of the common region PQRSTU?

(a) 49 cm2 

(b) 66 cm2 

(c) 132 cm2 

(d) 162 cm2 

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(c) 132 cm2.

There are 12 similar triangles in the figure forming a star, each with equal area. But a larger triangle ABC (or DEF) has only 9 smaller triangles. Out of the 9 triangles only 6 triangles are common.

∴ Area of common region PQRSTU 

= \(\frac{6}{9}\) x 198 cm = 132 cm2.

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