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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 29 Page 304

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

648ft^2

Practice makes perfect

We are told that a trapezoid has base lengths of 5 and 7 yards and a height of 12 yards. Let's see the diagram!

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

3ft/1yd Let's convert the measurements of our trapezoid!

	Yards	Conversion	Feet
Bottom Base	7	7* 3	21
Top Base	5	5* 3	15
Height	12	12* 3	36

We found that the bottom base of the trapezoid is 21 feet, the top base is 15 feet, and the height is 36 feet. 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* 36* ( 15+ 21)

▼

Evaluate right-hand side

Add terms

A=1/2* 36* 36

Multiply

A=1/2* 1296

MoveRightFacToNum

a/c* b = a* b/c

A=1296/2

Calculate quotient

A=648

The area of the trapezoid is 648 square feet.

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