Q22. - Algebra 1

Question

Find the area of each figure. Round to the nearest tenth.

Step-by-Step Solution

Answer

The area of the given figure is 23.1 square centimeters.

Step 1. State the formula.

The formula of the area of a trapezium is $A=\frac{1}{2}\left(a+b\right)h$, where A is the area, a and b are the lengths of the parallel sides, and h is the height of the trapezium.

Step 2. List the given data.

The given figure is a trapezium.

 

The lengths of the parallel sides are $5.2\mathrm{cm}$ and $8\mathrm{cm}$, while the height of the trapezium is $3.5\mathrm{cm}$.

 

Then, $a=5.2\mathrm{cm}$, $b=8\mathrm{cm}$ and $h=3.5\mathrm{cm}$.

Step 3. Calculate the area.

Put $a=5.2$, $b=8$ and $h=3.5$ in $A=\frac{1}{2}\left(a+b\right)h$ to get,

$$\begin{gathered} A=\frac{1}{2}\left(5.2+8\right)\left(3.5\right) \\ =\frac{1}{2}\left(13.2\right)\left(3.5\right) \\ =\left(6.6\right)\left(3.5\right) \\ =23.1 \end{gathered}$$

So, $A=23.1$.

Step 4. Determine the unit.

Since the units of lengths of the parallel sides and the height are given as centimeters, the unit of the area must be square centimeters.

 

So, the area of the given figure is 23.1 square centimeters. Note that this is already rounded to the nearest tenth.