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Big Ideas Math: Modeling Real Life, Grade 6

BI

Big Ideas Math: Modeling Real Life, Grade 6 View details

3. Areas of Trapezoids and Kites

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Exercise 26 Page 303

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

25 yards

Practice makes perfect

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

The trapezoid has base lengths of 23 and 25 yards with an area of 600 square yards. 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!

A=1/2h(b_1+b_2)

SubstituteValues

Substitute values

600=1/2h( 23+ 25)

▼

Solve for h

Add terms

600=1/2h(48)

CommutativePropMult

Commutative Property of Multiplication

600=1/2(48)h

MoveRightFacToNumOne

1/b* a = a/b

600=48/2h

Calculate quotient

600=24h

.LHS /24.=.RHS /24.

600/24=h

Calculate quotient

25=h

Rearrange equation

h=25

The height of the trapezoid is 25 yards.

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.

Subchapter links

Try It p.298-300

Self-Assessment for Concepts & Skills p.300

Self-Assessment for Problem Solving p.301

Review & Refresh p.302

Concepts, Skills, & Problem Solving p.302-304