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Chapter 10: Problem 53

Using the formula for the area of a rectangle, explain how the formula for the area of a parallelogram \((A=b h)\) is obtained.

Short Answer

Expert verified
The formula for the area of a parallelogram \(A=b*h\) is obtained through a geometric transformation into a rectangle of equal area.

Step by step solution

01

Understand the Area of a Rectangle

The formula for the area \(A\) of a rectangle is \(A = b*w\), where \(b\) is the base/length, and \(w\) is the width. The area is computed by multiplying the base (length) by the width (height).
02

Divide the Parallelogram into Two Triangles

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. You can divide the parallelogram into two congruent triangles by drawing a line from one corner to the opposite corner, creating two triangles.
03

Form a Rectangle

You can form a rectangle from the parallelogram by removing one of the triangles and placing it on the other side.
04

Derive the Formula for the Area of a Parallelogram

Once a rectangle is obtained from the parallelogram, it will have the same base \(b\) and height \(h\) as the parallelogram. Therefore, the area formula for a rectangle can now be applied to the parallelogram, which gives us \(A = b*h\) as the formula for finding the area of a parallelogram.

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Most popular questions from this chapter

Stonehenge, the famous "stone circle" in England, was built between 2750 B.C. and 1300 B.C. using solid stone blocks weighing over 99,000 pounds each. It required 550 people to pull a single stone up a ramp inclined at a \(9^{\circ}\) angle. Describe how right triangle trigonometry can be used to determine the distance the 550 workers had to drag a stone in order to raise it to a height of 30 feet.

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In Exercises 15-20, find the measure of the complement and the supplement of each angle. \(1^{\circ}\)

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In Exercises 15-20, find the measure of the complement and the supplement of each angle. \(15 \frac{1}{3} \circ\)
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