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daniel made a rectangle from 2 congruent trapezoids with bases 11 and 8 and height of 6. give the length, width, and area of the rectangle

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6 votes

Check the picture below.

daniel made a rectangle from 2 congruent trapezoids with bases 11 and 8 and height-example-1
User Lethargy
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Since the rectangle is made up of 2 congruent trapezoids, we can find the length and width of the rectangle by combining the lengths and widths of the trapezoids.

First, let's find the length of the rectangle:

The length of each trapezoid is the average of its bases:

length = (11 + 8) / 2 = 9.5

Since the trapezoids are congruent, the length of the rectangle is twice the length of a trapezoid:

length of rectangle = 2 * 9.5 = 19

Next, let's find the width of the rectangle:

The height of the trapezoids is the same as the height of the rectangle:

height = 6

The width of the rectangle is the same as the width of a trapezoid. To find the width of a trapezoid, we need to use the Pythagorean theorem, since the trapezoid has a height of 6 and bases of 11 and 8:

width = sqrt(6^2 + ((11-8)/2)^2) = sqrt(36 + 0.75) = sqrt(36.75)

So, the width of the rectangle is:

width = sqrt(36.75)

Finally, let's find the area of the rectangle:

area = length * width = 19 * sqrt(36.75) ≈ 87.83

Therefore, the length of the rectangle is 19 units, the width is approximately 6.07 units, and the area is approximately 87.83 square units.

User Yoven
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