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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

3. Areas of Regular Polygons

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Exercise 52 Page 634

Find the hypotenuse using the Pythagorean Theorem.

Perimeter: 24cm
Area: 24 cm^2

Practice makes perfect

We are asked to calculate the perimeter and area of the triangle using the values shown on the given diagram. Let's find those one at a time.

Finding the Perimeter

To find the perimeter, we need the length of all three sides of this right triangle.

Given the length of the two legs, we can use the Pythagorean Theorem to find the length of the hypotenuse.

a^2+b^2=c^2

a= 8, b= 6

8^2+ 6^2=c^2

▼

Simplify

Calculate power

64+36=c^2

Add terms

100=c^2

sqrt(LHS)=sqrt(RHS)

sqrt(100)=c

Calculate root

10=c

Rearrange equation

c=10

The hypotenuse is 10 cm. Notice that we only needed to consider a principal root because the hypotenuse is a measure. Now we can add all of the side lengths to find the perimeter. 6+ 8+ 10= 24cm

Finding the Area

In a right triangle, we can think of one leg as the base and the other leg as the height. Using these values, we can find the area using the formula for area of a triangle.

A=1/2bh

b= 8, h= 6

A=1/2( 8)( 6)

Multiply

A=1/2(48)

MoveRightFacToNumOne

1/b* a = a/b

A=48/2

Calculate quotient

A=24

The area of the triangle is 24 cm^2.

Subchapter links

Lesson Check p.631

Practice and Problem-Solving Exercises p.632-634

Standardized Test Prep p.634

Mixed Review p.634