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Big Ideas Math: Modeling Real Life, Grade 6
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Big Ideas Math: Modeling Real Life, Grade 6 View details
1. Multiplying Fractions
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Exercise 49 Page 51

The area of a trapezoid is one half of the product of its height and the sum of its bases.

20 kilometers

Practice makes perfect

From the picture we know some of the dimensions of the trapezoid. We want to find its height. Let's see the diagram!

Error loading image.
The trapezoid has base lengths of 14 and 4 kilometers with an area of 180 square kilometers. The area of a trapezoid is one</premium> 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!
A=1/2h(b_1+b_2)
SubstituteValues

Substitute values

180=1/2h( 14+ 4)
â–Ľ
Solve for h
AddTerms

Add terms

180=1/2h(18)
CommutativePropMult

Commutative Property of Multiplication

180=1/2(18)h
MoveRightFacToNumOne

1/b* a = a/b

180=18/2h
CalcQuot

Calculate quotient

180=9h
DivEqn

.LHS /9.=.RHS /9.

180/9=h
RearrangeEqn

Rearrange equation

h=180/9
CalcQuot

Calculate quotient

h=20
The height of the trapezoid is 20 kilometers.

Extra

 What We Know About Trapezoids

Let's review what we know about trapezoids.

  • A trapezoid is a quadrilateral with exactly 1 pair of parallel sides.
  • If a trapezoid has congruent legs, we call it an isosceles trapezoid.
  • In isosceles trapezoids, each pair of base angles is congruent.
  • Isosceles trapezoids have congruent diagonals.

Additionally, we have a theorem that tells us about the midsegment of a trapezoid.

Trapezoid Midsegment Theorem

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.

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