Pre-Algebra - Area of a Triangle

What is the area of the triangle?

Question_11

$\small 35$

$\small 70$

$\small 84$

$\small 42$

Explanation

Area of a triangle can be determined using the equation:

$\small A=\frac{1}{2}bh$

$\small A=\frac{1}{2}(14)(5)=35$

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?

$\frac{27}{2}$

None of these

Explanation

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

$\text{Area} =\frac{\text{base}\times \text{height}}{2}$

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

$b=h\div3=9\div3=3$

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

$\text{Area} =\frac{9\times 3}{2}$

$\text{Area} =\frac{27}{2}$

The fraction cannot be simplified.

Find the area of the triangle:
Problem_12

Explanation

The area of the triangle can be determined using the following equation:
$\small A=\frac{1}{2}bh$

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

$\small A=\frac{1}{2}(4)(12)=(2)(12)=24$

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

$6\textup{ in} ^2$

$12\textup{ in} ^2$

$8\textup{ in} ^2$

$4\textup{ in} ^2$

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,

$A=\frac{1}{2}( base \cdot height)$ .

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

This makes the equation

$\frac{1}{2}( 3\cdot 4)=\frac{1}{2}\cdot 12=\frac{12}{2}=6$

What is the area (in square feet) of a triangle with a base of feet and a height of feet?

Explanation

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

$Area =\frac{base\cdot height}{2}$

$Area =\frac{4\cdot 7}{2}$

Solve for the area of a right triangle if the hypotenuse is and the height is .

Explanation

Write the area formula for triangles.

$A=\frac{bh}{2}$

The base is unknown. To find this dimension, use the Pythagorean Theorem.

Substitute the hypotenuse into and the height into . Solve for the base.

Isolate the variable by subtracting on both sides of the equation.

Simplify the squares on the right side of the equation.

Subtract the left side.

Square root both sides of the equation to eliminate the square root.

$\sqrt{b^2} = \sqrt{64}$

We will only consider the positive root because length cannot be a negative value.

The base is 8. Substitute the base and height to find the area.

$A=\frac{(8)(6)}{2} = \frac{48}{2} =24$

The base of a triangle is inches, and the height of the triangle is inches. What is the area of the triangle?

square inches

Explanation

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

square inches

The base of a triangle is inches, and the height of the triangle is inches. What is the area of the triangle?

Explanation

To find the area of a triangle, multiply the base by the height, and divide by two.

The best answer is:

$A=\frac{b\times h}{2}=\frac{2\times 9}{2}=9$

Please use the following shape for the question. 5x3-adams-graphoc

What is the area of this shape?

$32.5\ in^{2}$

$25\ in^{2}$

$15\ in^{2}$

$40\ in^{2}$

$21\ in^{2}$

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.

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

$\small \small b = 4cm, h = 8cm$