Area of a Triangle - Pre-Algebra

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Find the area of the triangle:

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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$

What is the area of the triangle?

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Area of a triangle can be determined using the equation:

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

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

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

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

Plug the given values into the formula to solve:

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

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

Area=18

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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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 $\small 10 : feet$ .

Please use the following shape for the question.

What is the area of this shape?

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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.

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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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.

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

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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}$$

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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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 .

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

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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}$=6$

Find the area of this triangle:

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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$

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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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}$$ .

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

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

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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}$$ .

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

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

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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}$$ .

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

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

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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}$$ .

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

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

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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}$$ .

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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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$$

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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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

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

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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$

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

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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}$$

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

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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$