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Perimeter: 2.3ft
Area: 0.2ft^2
For the given polygon we will find its perimeter and its area one at a time. Let's do it!
The perimeter of a polygon is found by adding all of its side lengths. We know the lengths of two sides of our figure, but we are missing the other two. Since the polygon has exactly one pair of parallel sides, it is a trapezoid. Also, since the nonparallel sides are congruent, the trapezoid is an isosceles trapezoid.
Let's draw another height to construct a second right triangle on the right-hand side of the diagram.
The right triangles have congruent hypotenuses and one pair of congruent legs. Therefore, by the Hypotenuse Leg Theorem the triangles are congruent. Let x be the length of their base.
We have all of the information we need to calculate the perimeter of the polygon. Perimeter: 8+4+12+4=28in. Finally, to convert 28 inches into feet, we will use the fact that 12 inches is equal to 1 foot. We have to multiply our answer by the conversion factor 112. Perimeter: 28* 1/12≈ 2.3ft
The area of a trapezoid is one half the product of its base and the sum of its bases. In the given diagram, we can see that the lengths of the bases are 12 and 8 inches. Let's use a right triangle again to find the height h.
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Commutative Property of Multiplication
Multiply
Multiply fractions
a*b/c= a* b/c
Cancel out common factors
Identity Property of Multiplication
a* b/c=a/c* b
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Round to 1 decimal place(s)