How do you use Heron's formula to find the area of a triangle with sides of lengths #5 #, #6 #, and #7 #?

Answer 1

#"A"=14.7 "square units"# (rounded to one decimal place)

Heron's formula is:

#"A"=sqrt(s(s-a)(s-b)(s-c)#, where #s# is the semiperimeter.
The semiperimeter is the perimeter divided by 2, #s=(a+b+c)/2#.
Let side #a=5#, side #b=6#, and side #c=7#.
#s=(5+6+7)/2#
#s=18/2#
#s=9#

Substitute the known values into Heron's formula.

#"A"=sqrt(s(s-a)(s-b)(s-c)#
#"A"=sqrt(9(9-5)(9-6)(9-7)#

Simplify.

#"A"=sqrt(9(4)(3)(2))#
#"A"=sqrt(216)#
#"A"=14.7 "square units"# (rounded to one decimal place)
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To use Heron's formula to find the area of a triangle with side lengths (a), (b), and (c), where (s) is the semi-perimeter given by (s = \frac{a + b + c}{2}), you can use the following steps:

  1. Calculate the semi-perimeter: [ s = \frac{a + b + c}{2} ]

  2. Compute the area using Heron's formula: [ \text{Area} = \sqrt{s(s - a)(s - b)(s - c)} ]

For the given triangle with side lengths 5, 6, and 7:

  1. Calculate the semi-perimeter: [ s = \frac{5 + 6 + 7}{2} = 9 ]

  2. Compute the area using Heron's formula: [ \text{Area} = \sqrt{9(9 - 5)(9 - 6)(9 - 7)} = \sqrt{9 \times 4 \times 3 \times 2} = \sqrt{216} ]

Thus, the area of the triangle is ( \sqrt{216} ) square units.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7