Given:
Given that the irregular figure is broken into a triangle and a rectangle.
We need to determine the length b, the area of the triangle , the area of the rectangle and the area of the irregular figure.
Length of b:
The length of b , the base of the triangle is given by
![b=5-(2(1)/(3))](https://img.qammunity.org/2021/formulas/mathematics/college/a17zhw15atmvunl8dp5npuyh3bucvo0g57.png)
Simplifying, we get;
![b=5-(7)/(3)](https://img.qammunity.org/2021/formulas/mathematics/college/bkkjcubn38vxx85hoc2o84ekjm9t7h6w8m.png)
![b=(8)/(3) \ ft](https://img.qammunity.org/2021/formulas/mathematics/college/xdahl1zwrpzbvml5y2ft9mxmhf7wxgm2jy.png)
Thus, the length of the base of the triangle is
![(8)/(3) \ ft](https://img.qammunity.org/2021/formulas/mathematics/college/1rgl7rr6uvrji1w1iwb5az4ytbnzihteoy.png)
Area of the triangle:
The area of the triangle can be determined using the formula,
![A=(1)/(2)bh](https://img.qammunity.org/2021/formulas/mathematics/high-school/pmi4atjsmn0794m9nb42tnma5o4ubiy66a.png)
Substituting
and
, we get;
![A=(1)/(2)((8)/(3))(3)](https://img.qammunity.org/2021/formulas/mathematics/college/2zi8ogm867ds0k1b8qxwy2rynuziygfz5e.png)
![A=4 \ ft^2](https://img.qammunity.org/2021/formulas/mathematics/college/huynbyv26uc7pjt3zwga04zaw3wsburdde.png)
Thus, the area of the triangle is 4 square feet.
Area of the rectangle:
The area of the rectangle can be determined using the formula,
![A=lw](https://img.qammunity.org/2021/formulas/mathematics/middle-school/d9mfw1kn202ewxei9fp0lhh3q6jf79i72v.png)
where l = 5 ft,
, we get;
![A=5 * (4)/(3)](https://img.qammunity.org/2021/formulas/mathematics/college/ez19yswzjpjlmls1ab70v7hrgnvy1tavqe.png)
![A=(20)/(3) \ ft^2](https://img.qammunity.org/2021/formulas/mathematics/college/niv3gwn5ejtpm16tbmes21nlpte79oovm8.png)
Thus, the area of the rectangle is
![(20)/(3) \ ft^2](https://img.qammunity.org/2021/formulas/mathematics/college/i5ddapu4qmz4npkd3giogpf4y74byljjbv.png)
Area of the irregular figure:
The area of the irregular figure can be determined by adding the area of the triangle and the area of the rectangle.
Thus, we have;
Area = Area of the triangle + Area of the rectangle
Substituting the values, we have;
![Area = 4+(20)/(3)](https://img.qammunity.org/2021/formulas/mathematics/college/bnaihkuq2rm6f4aedtpte620jw5cd2abz4.png)
![Area = 10.667 \ ft^2](https://img.qammunity.org/2021/formulas/mathematics/college/uisxr2f2uusq843lknm83npzl8aj5r48nq.png)
Thus, the area of the irregular figure is 10.667 square feet.