Question

4.) figure 12.49 shows a trapezoid. This problem will help you find a formula for the area of the trapezoid and explain in several different ways why this formula is valid.a.) show how to combine two copies of the trapezoid and figure 12.49 to make a parallelogram. Then use the formula for the area of a parallelogram to deduce a formula for the area of the trapezoid. Explain your reasoningb.) show how to cut off portions of the top part of the trapezoid and combine these portions with the bottom part of the trapezoid so as to make one of several parallelograms or rectangles, each of which has one side of length 1/2h. use this method to deduce a formula for the area of the trapezoid. Explain your reasoning. c.) by subdividing the trapezoid into two triangles, as shown in figure 12.50, find a formula in terms of a, B, and each for the area of the trapezoid, and explain why your formula is valid.

Answer 1

Step 1 : Let's find the area of the parallelogram, as follows:

We have b and we have h, therefore, the area is:

b * h = Area of the parallelogram

Now we need to add the area of the two congruent right triangles, formed on the right to the parallelogram.

We know the height and for the base we will assume that a = b, therefore, the area of the triangles, would be

2b * h/2, but we have two triangles, then:

2b * h = Area of the two right triangles

In conclusion, the area of the trapezoid is:

A = (b1 + b2) * h¨* 1/2