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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

5. Rewriting Equations and Formulas

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Exercise 44 Page 42

Divide the regular polygon into $8$ congruent triangles.

Formula: $A = 4 b h$
Solution: $h = \frac{A}{4 b}$

Practice makes perfect

Let's divide the regular polygon into $8$ congruent triangles, where each has a base $b$ and a height $h .$

The area of the octagon is equal to the sum of the areas of the

8

identical triangles. We can calculate the area

A_{T}

of each of them using the formula for the area of a triangle. In the formula

b

stands for the base and

h

stands for the corresponding height of the triangle.

A_{T} = \frac{1}{2} b h

If we multiply the above expression by

8,

we get the the total area of the

8

triangles making up the polygon. Therefore, we get the formula for the area

A

of the regular polygon.

A = 8 A_{T} \Leftrightarrow A = 8 (\frac{1}{2} b h)

Let's simplify the expression.

A = 8 (\frac{1}{2} b h)

Remove parentheses

A = 8 \cdot \frac{1}{2} b h

MoveLeftFacToNumOne

$a \cdot \frac{1}{b} = \frac{a}{b}$

A = \frac{8}{2} b h

Calculate quotient

A = 4 b h

We want to solve this formula for the height

h,

which means we need to isolate it on one side.

A = 4 b h

$LHS / 4 b = RHS / 4 b$

\frac{A}{4 b} = h

Rearrange equation

h = \frac{A}{4 b}

Subchapter links

Communicate Your Answer p.35

Monitoring Progress p.36-39

Exercises p.40-42