Question

in the space provided, solve the following questions. for some questions, you need to fill in the missing pieces, and for others you need to solve the entire question. you can check your answers in the detailed solutions booklet (chapter 5, lesson 2). practice is important before you attempt the chapter 5 assignment. drilling for understanding 1. find the area of the following shapes. be sure to include units. a. b. hint: a hexagon is actually six triangles put together.

Explanation:

Step1: Recall triangle area formula

The formula for the area of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Calculate area of triangle a

For the triangle in part a, $b = 7$ cm and $h=8$ cm. So $A=\frac{1}{2}\times7\times8=28$ $cm^{2}$.

Step3: Recall hexagon - triangle relation

A regular hexagon can be divided into 6 congruent equilateral triangles. The area of one triangle with base $b = 6$ cm and height $h = 3$ cm is $A_{triangle}=\frac{1}{2}bh$.

Step4: Calculate area of one triangle in hexagon

Substitute $b = 6$ cm and $h = 3$ cm into the triangle - area formula: $A_{triangle}=\frac{1}{2}\times6\times3 = 9$ $cm^{2}$.

Step5: Calculate area of hexagon

Since the hexagon is made up of 6 such triangles, the area of the hexagon $A_{hexagon}=6\times A_{triangle}=6\times9 = 54$ $cm^{2}$.

Answer:

a. $28$ $cm^{2}$
b. $54$ $cm^{2}$