Break the figure into a rectangle and a triangle.  Use the dotted line as a guide. The rectangle has a length of 8 and a width of 6. The triangle has a base of 6 and width of 6.

Area of the rectangle:

\(\displaystyle A=l\times w\)

\(\displaystyle A=6\times 8=48\ ft^2\)

Area of the triangle:

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

\(\displaystyle A=\frac{1}{2}\times 6\times 6=3\times 6=18\ ft^2\)

Add them together:

\(\displaystyle A=48\ ft^2+18\ ft^2=66\ ft^2\)

\(\displaystyle A=\frac{1}{2}(b_1+b_2)(h)\)

\(\displaystyle A=\frac{1}{2}(6+10)(4)\)

\(\displaystyle A=\frac{1}{2}(16)(4)\)

\(\displaystyle A=(8)(4)=32\)

In order to find the area of the trapezoid, we must follow the formula below:

\(\displaystyle A=\frac{1}{2}(b_{1}+b_{2})*h\)

\(\displaystyle b_{1}=\) One of the bases of the trapezoid

\(\displaystyle b_{2}=\) The other base of the trapezoid

\(\displaystyle h=\) The height of the trapezoid

In this question, \(\displaystyle b_{1}=10\ in\), \(\displaystyle b_{2}=14\ in\), and \(\displaystyle h=6\ in\)

\(\displaystyle A=\frac{1}{2}(b_{1}+b_{2})*h\rightarrow A=\frac{1}{2}(10+14)*6\rightarrow\)

\(\displaystyle A=\frac{1}{2}(24)*6\rightarrow\)

\(\displaystyle A=12*6\rightarrow\)

\(\displaystyle A = 72\)

By following the formula and order of operations, we are able to solve the problem. The area of the trapezoid is 72 in.²

To find the area of a trapezoid, use this formula: \(\displaystyle area= \frac{base +base}{2}\times height\).

Use the information from the question to solve.

\(\displaystyle a= \frac{3cm+5cm}{2}\times4cm\)

\(\displaystyle a=\frac{8cm}{2}\times 4cm\)

\(\displaystyle a=4cm\times 4cm=16cm^2\)

The area is \(\displaystyle 16cm^{2}\).

The area of a trapezoid is equal to the sum of the bases, divided by 2, and then multiplied by the height:

\(\displaystyle Area=\frac{base+base}{2}\cdot height\)

\(\displaystyle \frac{5+11}{2}\cdot 6\)

\(\displaystyle \frac{16}{2}\cdot 6\)

\(\displaystyle 8\cdot 6\)

\(\displaystyle 48\)

The formula to calculate the area of a trapezoid is: 

\(\displaystyle A = \frac{base + base}{2}\times height\)

\(\displaystyle A = \frac{6cm+8cm}{2cm}\times5cm\)

\(\displaystyle A= \frac{14cm}{2cm}\times5cm\)

\(\displaystyle A= 7cm\times5cm\)

To solve, simply use the formula for the area of a trapezoid. Thus,

\(\displaystyle A=\frac{1}{2}(B1+B2)h=\frac{1}{2}(4+6)*5=\frac{1}{2}*10*5=25\)

To solve, simply use the formula for the area of a trapezoid. Thus,

\(\displaystyle A=\frac{1}{2}(b1+b2)h=\frac{1}{2}(5+4)*6=\frac{1}{2}*9*6=27\)

Recall the formula for finding the area of a trapezoid:

\(\displaystyle \text{Area}=\frac{base_1+base_2}{2}\times(height)\)

Now, plug in the values for the bases and the height to find the area.

\(\displaystyle \text{Area}=\frac{9+30}{2}\times(15)=292.5\)

Recall the formula for finding the area of a trapezoid:

\(\displaystyle \text{Area}=\frac{base_1+base_2}{2}\times(height)\)

Now, plug in the values for the bases and the height to find the area.

\(\displaystyle \text{Area}=\frac{15+30}{2}\times(25)=562.5\)