Question

Please help! Tysm! Picture of figure is attached.

Reasoning in the diagram at the right, K, L, and M are the midpoints of the sides of AABC. The vertices of the three small purple triangles are the midpoints of the sides of AKBL, AAKM, and AMLC. The perimeter of AABC is 24 cm. What is the perimeter of the shaded region? ​

Answer 1

Explanation:

Notice that KM = 0.5BC, KL = 0.5AC

and ML = 0.5AB. Therefore the perimeter of triangle KLM is half of the perimeter of triangle ABC. => 0.5 * 24cm = 12cm.

Each of the 3 purple triangles have perimeters which are 1/4 of the perimeter of triangle ABC. (Their vertices are midpoints of midpoints => 1/2 * 1/2)

Perimeter of 3 small purple triangles

= 3 * [24cm * (1/4)]

= 3 * 6cm = 18cm.

Hence Total perimeter of shaded parts

= 12cm + 18cm = 30cm.