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The area of a trapezoid is one half of the product of its height and the sum of its bases.
4 mm
From the picture we know some of the dimensions of the trapezoid. We want to find its height. Let's see the diagram!
Let's rotate the figures to help us recognize the dimensions.
The trapezoid has base lengths of 3 and 7 35 millimeters with an area of 21 15 square millimeters. The area of a trapezoid is one half the product of its height and the sum of its bases. A=1/2h(b_1+b_2) We can substitute the known values into this formula and solve for the height h. Let's do it!
Substitute values
Add terms
a bc=a* c+b/c
Multiply
Add terms
Multiply fractions
Multiply
LHS * 10/53=RHS* 10/53
Multiply fractions
Cross out common factors
Simplify quotient
Rewrite 106 as 53* 2
Rewrite 10 as 5* 2
Cross out common factors
Simplify quotient
Rearrange equation
The height of the trapezoid is 4 millimeters.
Additionally, we have a theorem that tells us about the midsegment of a trapezoid.
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Trapezoid Midsegment Theorem |
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The midsegment of a trapezoid is parallel to each base and it has a measure of one half the sum of the lengths of the bases. |