Beginning Algebra, 11th Edition

SECTION 8.6 Solving Equations with Radicals 539

EXERCISES 79 – 84

FOR INDIVIDUAL OR GROUP WORK

The most common formula for the area of a triangle is where bis the length

of the base and his the height. What if the height is not known?

Heron’s formulaallows us to calculate the area of a triangle if we know the

lengths of the sides a, b, and c. First, let sequal the semiperimeter,which is one-half

the perimeter.

The area is given by the formula

The familiar 3-4-5 right triangle has area square units, calculated

with the familiar formula. From Heron’s formula, , and

square units, as expected.

Consider the figure below, andwork Exercises 79 – 84 in order.

79.The lengths of the sides of the entire triangle are 7, 7,

and 12. Find the semiperimeter s.

80.Now use Heron’s formula to find the area of the

entire triangle. Write it as a simplified radical.

81.Find the value of hby using the Pythagorean theorem.

82.Find the area of each of the congruent right triangles forming the entire triangle by

using the formula

83.Double your result from Exercise 82to determine the area of the entire triangle.

84.How do your answers in Exercises 80 and 83compare?

a=^12 bh.

a= 2616 - 3216 - 4216 - 52 = 236 = 6

s=^12 13 + 4 + 52 = 6

a=^12 132142 = 6

a= 2 s 1 s-a 21 s-b 21 s-c 2.

a

s=

1

2

1 a+b+c 2

a=^12 bh,

RELATING CONCEPTS

6 6

12

77

h

Simplify each expression. Write the answer in exponential form with only positive exponents.
See Sections 5.1 and 5.2.

1 m^224 m-^1

1 m^32 -^1

1 c^322 c^4

1 c-^123

a

2 y^3

y-^1

b

• 2
  a

p

3

b

• 2

12 x^32 -^1

a-^2 a^3

a^4

15223 3 -^4 # 3 -^1

PREVIEW EXERCISES

78.The Khufu Pyramid in Giza (also known as
the Cheops Pyramid) was built in about
2566 B.C. to a height, at that time, of 481 ft.
It is now only 449 ft high. How far would
one of the original builders of the pyramid
have been able to see from the top of the
pyramid? (Source:www.archaeology.com)