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Question

A side of a triangle is divided into three congruent parts. Two lines, parallel to another side of the triangle, are drawn through each dividing point. Find the area of the quadrilaterals formed by those lines if the area of the original triangle is 24.

No videos please.

Answer 1

Draw and label a diagram

Draw the parallel lines parallel to the base

Label the lower line "p".

Label the upper line "u".

Recall the relation of the areas of similar figures to scale fator.

The area of the part of the triangle above line "p" is 4 / 9 of the entire triangle,

The are of the part of the triangle above the "u":line is 1 / 9 of the entire triangle.

The area of the quadrilateral is the area above the p minus the area above the u.

(4 / 9)(24) - (1 / 9)(24)

(24)(3 / 9)

(24)(1 /3)

8