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
[tex]b=5-(2\frac{1}{3})[/tex]
Simplifying, we get;
[tex]b=5-\frac{7}{3}[/tex]
[tex]b=\frac{8}{3} \ ft[/tex]
Thus, the length of the base of the triangle is [tex]\frac{8}{3} \ ft[/tex]
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]A=\frac{1}{2}bh[/tex]
Substituting [tex]b=\frac{8}{3} \ ft[/tex] and [tex]h=3 \ ft[/tex], we get;
[tex]A=\frac{1}{2}(\frac{8}{3})(3)[/tex]
[tex]A=4 \ ft^2[/tex]
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,
[tex]A=lw[/tex]
where l = 5 ft, [tex]w=1 \frac{1}{3}=\frac{4}{3} \ ft[/tex], we get;
[tex]A=5 \times \frac{4}{3}[/tex]
[tex]A=\frac{20}{3} \ ft^2[/tex]
Thus, the area of the rectangle is [tex]\frac{20}{3} \ ft^2[/tex]
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;
[tex]Area = 4+\frac{20}{3}[/tex]
[tex]Area = 10.667 \ ft^2[/tex]
Thus, the area of the irregular figure is 10.667 square feet.
