### All Precalculus Resources

## Example Questions

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

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

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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

Find the area of this triangle:

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 side lengths , , and ?

**Possible Answers:**

**Correct answer:**

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