Question

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 

Answer 1

(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 cm²  = 132 cm².