Question

In ΔABC, D and E are the mid points of AB and AC. If the area of ΔABC = 60 sq. cm. Show that the area of ΔADE = 15 sq. cm.

Answer 1

In ΔABC, D and E are the midpoints of AB and AC respectively.

We know that the line joining the midpoints of two sides of any triangle is parallel to the third side.

In ΔABC and ΔADE:

, and

Thus, ΔABC and ΔADE are similar triangles.

By Area theorem, the areas of two similar triangles are proportional to the squares of the corresponding sides.

Hence, the area of ΔADE is.