Question

determine the area of the trapezoid base 1: 10 in base 2: 6 in height: 5 in determine the area of the trapezoid base 1: 30 cm base 2: 22 cm height: 10 cm determine the area of the rhombus base: 6 in height: 4 in determine the area of the rhombus base: 9 in height: 2.5 in

Explanation:

Step1: Recall trapezoid area formula

The formula for the area of a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1$ and $b_2$ are the lengths of the bases and $h$ is the height.

Step2: Calculate first trapezoid area

For the trapezoid with $b_1 = 10$ in, $b_2=6$ in and $h = 5$ in, we substitute into the formula:
\[

$$\begin{align*} A_1&=\frac{(10 + 6)\times5}{2}\\ &=\frac{16\times5}{2}\\ &=\frac{80}{2}\\ &= 40\text{ in}^2 \end{align*}$$

\]

Step3: Calculate second trapezoid area

For the trapezoid with $b_1 = 30$ cm, $b_2 = 22$ cm and $h=10$ cm, we substitute into the formula:
\[

$$\begin{align*} A_2&=\frac{(30 + 22)\times10}{2}\\ &=\frac{52\times10}{2}\\ &=\frac{520}{2}\\ &=260\text{ cm}^2 \end{align*}$$

\]

Step4: Recall rhombus area formula

The formula for the area of a rhombus is $A = bh$, where $b$ is the base and $h$ is the height.

Step5: Calculate first rhombus area

For the rhombus with $b = 6$ in and $h = 4$ in, we have $A_3=6\times4=24\text{ in}^2$.

Step6: Calculate second rhombus area

For the rhombus with $b = 9$ in and $h = 2.5$ in, we have $A_4=9\times2.5 = 22.5\text{ in}^2$.

Answer:

Trapezoid 1 area: 40 in²
Trapezoid 2 area: 260 cm²
Rhombus 1 area: 24 in²
Rhombus 2 area: 22.5 in²