Question

Quadrilateral is a parallelogram. Its area is square units. Points A and B are the midpoints of sides CD and EF, respectively. What is the area of triangle ABC?

a) 1/4​ of the parallelogram's area
b) 1/2​ of the parallelogram's area
c) Equal to the parallelogram's area
d) Cannot be determined without additional information

Answer 1

The area of triangle ABC is 1/4 of the parallelogram's area.

Step-by-step explanation:

The area of triangle ABC can be found by using the formula for the area of a triangle: 1/2 × base × height. Since points A and B are the midpoints of sides CD and EF, they divide those sides into two equal halves. Therefore, the base of triangle ABC is half the length of side CD, and the height is half the length of side EF.

In a parallelogram, opposite sides are equal in length, so the base of triangle ABC is equal to half the length of side CD, and the height is equal to half the length of side EF.

If the area of the parallelogram is given as A square units, then the area of triangle ABC is 1/2 × (1/2 × CD) × (1/2 × EF). This simplifies to 1/4 × CD × EF. Therefore, the area of triangle ABC is 1/4 of the parallelogram's area, so the correct answer is a) 1/4 of the parallelogram's area.