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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 30 Page 304

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

approximately 355 square feet

Practice makes perfect

We are told that a trapezoid has base lengths of 3 and 8 meters and a height of 6 meters. Let's see the diagram!

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

3.28ft/1m Let's convert the measurements of our trapezoid!

	Meters	Conversion	Feet
Bottom Base	8	8* 3.28	≈ 26.24
Top Base	3	3* 3.28	≈ 9.84
Height	6	6* 3.28	≈ 19.68

We found that the bottom base of the trapezoid is about 26.24 feet, the top base is about 9.84 feet, and the height is about 19.68 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* 19.68* ( 9.84+ 26.24)

▼

Evaluate right-hand side

Add terms

A=1/2* 19.68* (36.08)

Multiply

A=355.0272

Round to 1 decimal place(s)

A≈ 355

The area of the trapezoid is approximately 355 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