Answer:
- rectangle: 30 ft²
- triangle: 12 ft²
- total: 42 ft²
Explanation:
You want the area of the composite figure consisting of a rectangle and a triangle.
Rectangle
The area of the rectangle is ...
A = LW
A = (5 ft)(6 ft) = 30 ft² . . . . rectangle area
Triangle
The base of the triangle is the difference in length of the horizontal segments:
b = 9 ft -5 ft = 4 ft
The area is given by the formula ...
A = 1/2bh
A = 1/2(4 ft)(6 ft) = 12 ft² . . . . triangle area
Total area
The area of the figure is the sum of the areas of its parts:
total area = rectangle area + triangle area
total area = 30 ft² +12 ft²
total area = 42 ft²
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Additional comment
The area of this trapezoid can also be found using the trapezoid formula:
A = 1/2(b1 +b2)h
A = 1/2(9 ft +5 ft)(6 ft) = 42 ft²
The rectangle is shown in the figure as 5 ft wide and 6 ft tall. It does not matter which of these dimensions you call the length and which you call the width. Their product is the same either way.