Answer:
- Area: 130 square units.
- Perimeter: 58 units.
Step-by-step explanation:
You want the area and perimeter of a composite figure consisting of an isosceles trapezoid with bases 23 and 11, height 8, and a notch 2 deep and 3 wide cut from the top base.
Trapezoid
Ignoring the cutout for the moment, the area of the trapezoid is ...
A = 1/2(b1 +b2)h
A = 1/2(23 +11)(8) = 136 . . . . square units
The cutout at the top is 2 deep and 3 wide, so has an area of ...
A =LW
A = 2(3) = 6 . . . . square units
The remaining area of the figure is ...
136 -6 = 130 . . . . square units.
Perimeter
The perimeter is the sum of the side lengths. Working clockwise from lower left, we have ...
P = 10 +4 +2 +3 +2 +4 +10 +23 = 58
The perimeter of the figure is 58 units.
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Additional comment
The width of the top base is the sum of the lengths of the horizontal segments there: 4 +3 +4 = 11. We have used this number in our summary of the problem statement.
