Answer:
- area: 27.8 square units
- perimeter: 21.2 units
Step-by-step explanation:
The area of a compound figure is the sum of the areas of its parts. The perimeter is the sum of the lengths of all of the edges.
<h3>Area</h3>
This compound figure is conveniently divided into a semicircle of radius 2.5 and a trapezoid with bases 5 and 7, and height 3.
<u>Semicircle</u>
The area of the semicircle is half the area of a circle with the same radius. It will be ...
A = 1/2πr²
A = 1/2π(2.5²) = 3.125π . . . . square units
<u>Trapezoid</u>
The area of the trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
A = (1/2)(5 +7)(3) = 18 . . . . square units
Then the total area of the figure is ...
3.125π +18 ≈ 27.8 . . . . square units
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Perimeter
The perimeter will be the sum of the lengths of the straight line segments and the length of the semicircular arc.
<u>Arc</u>
The arc length is half the circumference of the circle, so is ...
arc = 1/2(2πr) = πr = 2.5π . . . . units
<u>Diagonal segments</u>
The figure is bounded by two congruent line segments that are each the hypotenuse of a triangle 1 unit wide and 3 units high. The Pythagorean theorem tells us that length is ...
diagonal length = √(1² +3²) = √10 . . . . units
The two diagonal sides have a total length of 2√10 units.
<u>Horizontal segments</u>
The figure is bounded by two congruent horizontal segments of length 1 unit each, and one horizontal segment of length 5 units. Their total length is ...
horizontal length = 1 + 1 + 5 = 7 . . . . units
The total perimeter is ...
perimeter = horizontal length + diagonal length + arc length
7 +2√10 +2.5π ≈ 21.2 . . . . units
