Both Trapezoids are similar. The area of the smaller trapezoid is 26 ft. square. Which is the best approximation for the area of the larger trapezoid if the base is 20 ft. in the smaller trapezoid base is 16 ft.
Area of similar figures is proportional to the square of the length of corresponding sides.
26 ft² : A ft²
= (16)² : (20)²
Cross multiply to get:
16²*A = 26 * 20²
A = (20÷16)² * 26 ft²
= 40.6 ft² (approx.)
7.
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Find the area of the equilateral triangle.
To find the area of the larger trapezoid, we can use the concept of similarity. Similar shapes have corresponding sides that are in proportion to each other.
Given that the smaller trapezoid has a base of 16 ft. and an area of 26 ft², we need to find the scale factor between the two trapezoids.
The formula for the area of a trapezoid is:
Area = height * (sum of bases) / 2
Let's calculate the height of the smaller trapezoid first.
Area of smaller trapezoid = 26 ft²
Base1 = 16 ft.
Base2 = 20 ft. (given for the larger trapezoid)
Using the formula for the area, we can rearrange it to solve for the height:
Height = (2 * Area) / (Base1 + Base2)
Height = (2 * 26) / (16 + 20)
Height = 52 / 36
Height ≈ 1.44 ft.
Now, we can find the scale factor between the two trapezoids by comparing the bases:
Scale factor = Base2 of larger trapezoid / Base1 of smaller trapezoid
Scale factor = 20 ft. / 16 ft.
Scale factor = 1.25
Finally, we can calculate the area of the larger trapezoid:
Area of larger trapezoid = Scale factor^2 * Area of smaller trapezoid
Area of larger trapezoid ≈ (1.25^2) * 26 ft²
Area of larger trapezoid ≈ 1.56 * 26 ft²
Area of larger trapezoid ≈ 40.56 ft²
Therefore, the best approximation for the area of the larger trapezoid is 40.56 ft².
To find the best approximation for the area of the larger trapezoid, you can use the concept of similarity between the two trapezoids. When two trapezoids are similar, their corresponding sides are proportional, and the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.
In this case, the ratio of the bases of the two trapezoids is 20 ft. (larger trapezoid) to 16 ft. (smaller trapezoid), which simplifies to 5:4.
Since the area of the smaller trapezoid is given as 26 ft.², you can find the best approximation for the area of the larger trapezoid by finding the square of the ratio of their bases and multiplying it by the area of the smaller trapezoid.
The ratio of the bases squared is (5/4)² = 25/16.
Therefore, the best approximation for the area of the larger trapezoid is (25/16) * 26 ft.².
Simplifying the expression, you multiply 25/16 by 26: (25/16) * 26 = 162.5.
So, the best approximation for the area of the larger trapezoid is approximately 162.5 ft.².