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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 28 Page 304

Use a conversion factor to convert from inches to feet. The area of a trapezoid is one half of the product of its height and the sum of its bases.

7/16ft^2

Practice makes perfect

We are told that a trapezoid has base lengths of 9 and 12 inches and a height of 6 inches. Let's see the diagram!

Before we substitute these two values into the formula for the area of a trapezoid, let's convert the inches into feet. Converting between inches and feet will involve using a conversion factor.

1ft/12in. Let's convert the measurements of our trapezoid!

	Inches	Conversion	Feet
Bottom Base	12	12* 1/12	1
Top Base	9	9* 1/12	3/4
Height	6	6* 1/12	1/2

We found that the bottom base of the trapezoid is 1 foot, the top base is 34 foot, and the height is 12 foot. Now we can substitute these values into the formula for the area of a trapezoid. Let's do it!

A=1/2h(b_1+b_2)

SubstituteValues

Substitute values

A=1/2* 1/2* ( 3/4+ 1)

▼

Simplify

a = 4* a/4

A=1/2* 1/2* (3/4+4/4)

Add fractions

A=1/2* 1/2* (3+4/4)

Add terms

A=1/2* 1/2* (7/4)

Multiply fractions

A=1* 1* 7/2* 2* 4

Multiply

A=7/16

The area of the trapezoid is 716 square foot.

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