body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

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

Finish the assignment

Continue to next subchapter

Exercise 27 Page 303

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

4 mm

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!

Let's rotate the figures to help us recognize the dimensions. The trapezoid has base lengths of 3 and 7 35 millimeters with an area of 21 15 square millimeters. 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

21 15=1/2h( 7 35+ 3)

▼

Solve for h

Add terms

21 15=1/2h(10 35)

a bc=a* c+b/c

21* 5+1/5=1/2h (10* 5+3/5)

Multiply

105+1/5 = 1/2h(50+3/5)

Add terms

106/5 = 1/2h(53/5)

Multiply fractions

106/5=h1* 53/2* 5

Multiply

106/5=h53/10

LHS * 10/53=RHS* 10/53

106/5* 10/53=h53/10* 10/53

Multiply fractions

106* 10/5* 53=h 53* 10/10* 53

Cross out common factors

106* 10/5* 53=h 53* 10/10* 53

Simplify quotient

106* 10/5* 53=h

Rewrite 106 as 53* 2

53* 2* 10/5* 53=h

Rewrite 10 as 5* 2

53* 2* 2* 5/5* 53=h

Cross out common factors

53* 2* 2* 5/5* 53=h

Simplify quotient

4=h

Rearrange equation

h=4

The height of the trapezoid is 4 millimeters.

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