# Precalculus : Area of a Triangle

## Example Questions

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### Example Question #1 : Use Trigonometric Functions To Calculate The Area Of A Triangle

In triangle , , , and .  Find the area of the triangle.

Explanation:

When given the lengths of two sides and the measure of the angle included by the two sides, the area formula is:

Plugging in the given values we are able to calculate the area.

### Example Question #2 : Area Of A Triangle

Find the area of this triangle:

Explanation:

To find the area, use the formula associated with side, angle, side triangles which states,

where  and  are side lengths and  is the included angle.

In our case,

.

Plug the values into the area formula and solve.

### Example Question #3 : Area Of A Triangle

Find the area of this triangle:

Explanation:

Use the area formula to find area that is associated with the side angle side theorem for triangles.

where  and  are side lengths and  is the included angle.

Plugging these values into the formula above, we arrive at our final answer.

### Example Question #4 : Area Of A Triangle

Find the area of this triangle:

Explanation:

To solve, use the formula for area that is associated with the side angle side theorem for triangles,

where  and  are side lengths and  is the included angle.

Here we are using and not since that is the angle between  and .

Therefore,

.

Plugging the above values into the area formula we arrive at our final answer.

### Example Question #5 : Area Of A Triangle

Find the area of this triangle:

Explanation:

Find the area using the formula associated the side angle side theorem of a triangle,

where  and  are side lengths and  is the included angle.

In this particular case,

therefore the area is found to be,

.

### Example Question #6 : Area Of A Triangle

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

Explanation:

Use the Heron's Formula:

Solve for .

Solve for the area.

### Example Question #7 : 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 #1 : Area Of A Triangle

What is the area of a triangle with sides , 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 #9 : Area Of A Triangle

What is the area of a triangle with side lengths of , 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 #10 : 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

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