Precalculus : Find the Area of a Triangle Using Heron's Formula (SSS)

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 : Find The Area Of A Triangle Using Heron's Formula (Sss)

Find the exact area of a triangle with side lengths of , , and .

Possible Answers:

Correct answer:

Explanation:

Use the Heron's Formula:

Solve for .

Solve for the area.

Example Question #2 : Find The Area Of A Triangle Using Heron's Formula (Sss)

What is the area of a triangle with side lengths  , , and  ?

 

Possible Answers:

Correct answer:

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

Example Question #3 : Find The Area Of A Triangle Using Heron's Formula (Sss)

What is the area of a triangle with sides , and  ?

Possible Answers:

Correct answer:

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

Example Question #4 : Find The Area Of A Triangle Using Heron's Formula (Sss)

What is the area of a triangle with side lengths of , and  ?

Possible Answers:

Correct answer:

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

Example Question #5 : Find The Area Of A Triangle Using Heron's Formula (Sss)

What is the area of a triangle with side lengths , and  ?

Possible Answers:

Correct answer:

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

Example Question #6 : Find The Area Of A Triangle Using Heron's Formula (Sss)

What is the area of a triangle with side lengths , and  ?

Possible Answers:

Correct answer:

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

Example Question #7 : Find The Area Of A Triangle Using Heron's Formula (Sss)

What is the area of a triangle with side lengths , and  ?

Possible Answers:

Correct answer:

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

Example Question #8 : Find The Area Of A Triangle Using Heron's Formula (Sss)

What is the area of a triangle with side lengths , and  ?

Possible Answers:

Correct answer:

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

Example Question #9 : Find The Area Of A Triangle Using Heron's Formula (Sss)

What is the area of a triangle if the sides of a triangle are , and  ?

Possible Answers:

Correct answer:

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

 

Example Question #10 : Find The Area Of A Triangle Using Heron's Formula (Sss)

The triangular fence of the T-rex in Jurassic park has sides a,b, and c measuring 100m, 110m, and 120m respectively. What is area of its enclosure? 

Possible Answers:

Correct answer:

Explanation:

Use Heron's formula to calculate the area: 

 

A, B, and C are side lengths and s is calculated by:

.

Calculate s:

Plug side lengths and s into Heron's formula:

 

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