Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 1 - Solving Linear Equations - 1.5 - Rewriting Equations and Formulas - Exercises - Page 42: 43

Answer

$A=\frac 52 bh$ $h=\frac{2A}{5b}$

Work Step by Step

Decompose the polygon in $5$ equal triangles with common vertex at center. Each triangle has height $h$ and base $b$, so each triangle area is: $$A_1=\frac 12 bh$$ Area of whole polygon: $$A=5A_1=5\cdot \frac 12 bh=\frac 52 bh$$ Solve for $h$: $$h=A\div\left(\frac 52 b\right)=A\cdot \frac{2}{5b}=\frac{2A}{5b}$$
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