Area of a Triangle - Pre-Algebra

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Question

What is the area of a triangle with a base of and a height of ?

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Answer

The formula for the area of a triangle is $\dpi{100} Area=\frac{1}{2}\times base\times height$ .

Plug the given values into the formula to solve:

$\dpi{100} Area=\frac{1}{2}\times 12\times 3$

$\dpi{100} Area=\frac{1}{2}\times 36$

$\dpi{100} Area=18$

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Question

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?

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Answer

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

$\small \frac{b\cdot h}{2}$

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

$\small \frac{8\cdot h}{2}=40$

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:

$\small \frac{8\cdot h}{2}\cdot 2=8\cdot h$

The right-hand side simplifies to:

$\small 40\cdot 2=80$

Now our equation can be rewritten as:

$\small 8\cdot h=80$

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

$\small \frac{8\cdot h}{8}=h$

$\small \frac{80}{8}=10$

$\small h=10$

Therefore, the height of the triangle is $\small 10 : feet$ .

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Question

Please use the following shape for the question.

What is the area of this shape?

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Answer

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.

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Question

Find the area of the triangle:

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Answer

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.

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

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Question

What is the area of the triangle?

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Answer

Area of a triangle can be determined using the equation:

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

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

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Question

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?

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Answer

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.

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Question

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

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Answer

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

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

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

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Question

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

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Answer

The correct answer is $Area = 25 in^{2}$ .

The formula for the area of a triangle is $\frac{1}{2}\times base\times height$ .

To solve the equation, plug in the base and height: $\frac{1}{2} \cdot5\cdot10$

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

The units for area are always squared, so the unit is $in^{2}$ .

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Question

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

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Answer

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

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

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Question

Find the area of this triangle:

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Answer

The formula for the area of a triangle is $A = \frac{1}{2}(base)(height)$ . In this case, the base is 11 and the height is 9. So, we're multiplying $\frac{1}{2}119 = \frac{1}{2}*99 = 49.5$

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Question

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

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

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Answer

The area of triangle is found using the formula

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

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

$\small A = \frac{1}{2}(4)(8) = 16$ .

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

Thus, our final answer is $\small 16cm^{2}$ .

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Question

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

$\small b = 9cm , h = 4cm$

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Answer

The area of triangle is found using the formula

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

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

$\small \small \small A = \frac{1}{2}(9)(4) = 18cm^{2}$ .

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

Thus, our final answer is $\small 18cm^{2}$ .

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Question

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

$\small b = 4cm , h = 10cm$

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Answer

The area of triangle is found using the formula

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

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

$\small A = \frac{1}{2}(4)(10) = 20cm^{2}$ .

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

Thus, our final answer is $\small 20cm^{2}$ .

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Question

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

$\small b = 10cm, h = 30cm$

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Answer

The area of triangle is found using the formula

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

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

$\small \small A = \frac{1}{2}(10)(30) = 150cm^{2}$ .

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

Thus, our final answer is $\small 150cm^{2}$ .

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Question

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

$\small b = 13cm, h = 16cm$

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Answer

The area of triangle is found using the formula

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

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

$\small \small A = \frac{1}{2}(13)(16) = 104$ .

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

Thus, our final answer is $\small \small 104cm^{2}$ .

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Question

What is the area of an isoceles triangle that has a base length of 18 inches, side lengths of 15 inches and a vertical height of 12 inches?

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Answer

Area of a triangle is:- $\frac{1}{2}* \textup{base} * \textup{vertical height}$

Area is in Square Units.

$\frac{1}{2} * 18 *12 =$

$108\ \textup{in}^2$

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Question

If Joan has a triangle-shaped plot for her garden, with the base measuring 3 ft and the heigh measuring 4 ft, what is the area of her garden?

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Answer

To find the area of a triangle, use the formula $\frac{1}{2}(b\times h)$ or $\frac{b\times h}{2}$

$\frac{1}{2}$

$\frac{1}{2}(12)=$

square ft

or

$\frac{(3x4)}{2}=$

$\frac{12}{2}=$

square ft

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Question

The base of the triangle is . The height of the triangle is . What is the area of the triangle?

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Answer

Write the area for a triangle.

$A=\frac{1}{2}\times B\times H$

Substitute the base and height.

$A=\frac{1}{2}\times 4\times (x+4) = 2(x+4) = 2x+8$

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Question

Find the area of a triangle with a base of and a height of .

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Answer

Write the formula for the area of a triangle.

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

Substitute the base and height.

$A=\frac{5\times11}{2} = \frac{55}{2}$

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Question

What is the area of a right triangle if the hypotenuse is five, and a base leg is four?

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Answer

Write the area for a right triangle.

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

The height is unknown. In order to solve for the height, use the Pythagorean Theorem to find the unknown length.

The height of the triangle is three. Substitute both leg dimensions to find the area.

$A=\frac{1}{2}(3\times 4) = 6$

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