Precalculus : Use trigonometric functions to calculate the area of a triangle

Example Questions

Example Question #11 : Area Of A Triangle

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

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 #12 : Area Of A Triangle

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

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 #11 : Area Of A Triangle

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

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 #14 : Area Of A Triangle

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

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 #15 : Area Of A Triangle

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?

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:

Example Question #11 : Area Of A Triangle

Find the area of this triangle:

Explanation:

Use Heron's Formula

where

and

we can find  to be:

.

From here, plug in all our known values and solve.

Example Question #17 : Area Of A Triangle

Find the area of this triangle:

Explanation:

To find the area, use Heron's Formula,

where

and

.

Here,

.

Now plug in all known values and solve.

Example Question #18 : Area Of A Triangle

Find the area of this triangle:

Explanation:

To solve, use Heron's Formula,

where , , and  are the side lengths and

.

In this particular case,

thus,

.

Plugging these values into the Heron's Formula we arrive at our answer.

Example Question #19 : Area Of A Triangle

Find the area of this triangle:

Explanation:

To find the area, use Heron's Formula

where , , and  are the side lengths and .

In this case,

thus,

.

Now plugging these values into the Heron's Formula, we arrive at our final answer,

Example Question #20 : Area Of A Triangle

Given a triangle with lengths 4,8, and 10, find the area of the triangle.