# Pre-Algebra : Area of a Triangle

## Example Questions

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

Find the area of the triangle:

Possible Answers:

Correct answer:

Explanation:

The area of the triangle can be determined using the following equation:

The base is the side of the triangle that is intersected by the height.

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

The length of the base of a triangle is  inches. The height of the triangle is  inches. Find the area of the triangle.

Possible Answers:

Correct answer:

Explanation:

The correct answer is .

The formula for the area of a triangle is .

To solve the equation, plug in the base and height:

Once you multiply these three numbers, the answer you find is .

The units for area are always squared, so the unit is .

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

If a right triangle has dimensions of  inches by  inches by  inches, what is the area?

Possible Answers:

Correct answer:

Explanation:

The question is asking you to find the area of a right triangle.

First you must know the equation to find the area of a triangle,

.

A right triangle is special because the height and base are always the two smallest dimensions.

This makes the equation

### Example Question #3 : How To Find The Area Of A Triangle

Please use the following shape for the question.

What is the area of this shape?

Possible Answers:

Correct answer:

Explanation:

From this shape we are able to see that we have a square and a triangle, so lets split it into the two shapes to solve the problem. We know we have a square based on the 90 degree angles placed in the four corners of our quadrilateral.

Since we know the first part of our shape is a square, to find the area of the square we just need to take the length and multiply it by the width. Squares have equilateral sides so we just take 5 times 5, which gives us 25 inches squared.

We now know the area of the square portion of our shape. Next we need to find the area of our right triangle. Since we know that the shape below the triangle is square, we are able to know the base of the triangle as being 5 inches, because that base is a part of the square's side.

To find the area of the triangle we must take the base, which in this case is 5 inches, and multipy it by the height, then divide by 2. The height is 3 inches, so 5 times 3 is 15. Then, 15 divided by 2 is 7.5.

We now know both the area of the square and the triangle portions of our shape. The square is 25 inches squared and the triangle is 7.5 inches squared. All that is remaining is to added the areas to find the total area. Doing this gives us 32.5 inches squared.

### Example Question #5 : How To Find The Area Of A Triangle

What is the area of the triangle?

Possible Answers:

Correct answer:

Explanation:

Area of a triangle can be determined using the equation:

### Example Question #3 : How To Find The Area Of A Triangle

Bill paints a triangle on his wall that has a base parallel to the ground that runs from one end of the wall to the other. If the base of the wall is 8 feet, and the triangle covers 40 square feet of wall, what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

In order to find the area of a triangle, we multiply the base by the height, and then divide by 2.

In this problem we are given the base and the area, which allows us to write an equation using as our variable.

Multiply both sides by two, which allows us to eliminate the two from the left side of our fraction.

The left-hand side simplifies to:

The right-hand side simplifies to:

Now our equation can be rewritten as:

Next we divide by 8 on both sides to isolate the variable:

Therefore, the height of the triangle is .

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

A triangle has a height of 9 inches and a base that is one third as long as the height. What is the area of the triangle, in square inches?

Possible Answers:

None of these

Correct answer:

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by 2.

Given that the height is 9 inches, and the base is one third of the height, the base will be 3 inches.

We now have both the base (3) and height (9) of the triangle. We can use the equation to solve for the area.

The fraction cannot be simplified.

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

Find the area of this triangle:

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a triangle is . In this case, the base is 11 and the height is 9. So, we're multiplying

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

Given the following measurements of a triangle: base (b) and height (h), find the area.

Possible Answers:

Correct answer:

Explanation:

The area of triangle is found using the formula

.

Provided with the base and the height, all we need to do is plug in the values and solve for A.

.

Since this is asking for the area of a shape, the units are squared.

Thus, our final answer is

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

Given the following measurements of a triangle: base (b) and height (h), find the area.

Possible Answers:

Correct answer:

Explanation:

The area of triangle is found using the formula

.

Provided with the base and the height, all we need to do is plug in the values and solve for A.

.

Since this is asking for the area of a shape, the units are squared.

Thus, our final answer is

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