Question

1 Serek is showing how to model the area

formula of a triangle

1) Original triangle

2) Create a congruent triangle.

Rotate it then join it to the original

triangle, forming a parallelogram.

3) Decompose the parallelogram

into a right triangle and a trapezoid.

4) Rearrange the triangle and

trapezoid to form a rectangle.

Which of these steps will identify the area

of the original triangle?

A Find the total area of the trapezoid

B Find half the area of the rectangle

C Find half the area of the trapezoid

D Find the area of the shaded triangle

5.80

Answer 1

Find half the area of the rectangle

Explanation:

Given

See attachment for the Serek's steps

Required

Which can be used to determine the area of the original triangle

To do this, we simply analyze each step.

At step 2, where he joined two congruent triangles to form a parallelogram.

Half the area of the parallelogram will give the area of the original triangle (since both triangles are equal)

At step 3, where he decomposed the parallelogram to a trapezoid and a right triangle.

Half the sum of the areas of the resulting shapes (trapezoid and right triangle) will equal to the area of the original triangle but half the area of each shape will not amount to the area of the original triangle

At step 4, where the right triangle and the trapezoid are merged to form a rectangle.

The area of the rectangle will equal to the area of the parallelogram in step (2).

So, half the area of the rectangle will equal to the area of the triangle.

Hence, (b) is correct