How to find the area of a triangle - ISEE Lower Level (grades 5-6) Mathematics Achievement

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Question

The base of triangle ABC is $\dpi{100} 6\ cm$ , it's height $\dpi{100} 12\ cm$ . What is the triangle's area?

Answer

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

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Question

What is the area of a triangle that has a base of $14\ cm$ and a height of $5\ cm.$

Answer

In order to find the area of a triangle, we must use the formula

$\frac{1}{2}\left ( b\cdot h \right )$

So the first thing we must do is multiply the base and height.

$14cm\cdot 5 cm = 70 cm^{2}$

The next thing we must do is find $\frac{1}{2}$ of through multiplication.

$\small \frac{1}{2}$ $\cdot 70 cm^{2}=35 cm^{2}$

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Question

Find the height of the triangle.

If the base of a triangle is and the area is , what is the height of the triangle?

Answer

Area of a triangle is

$\frac{1}{2}base\times height$

Set up the equation, then solve:

$\frac{1}{2}(6mm)\times h = 12mm$

$(3mm)\times h=12mm$

so

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Question

Find the area of the triangle:

Answer

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

$A=\frac{1}{2}(10)(7)$

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Question

A triangle has an area of 36 in.2. if its base is 6 in., what is its height?

Answer

To find the height of the triangle, you must need to plug in what you know (the area and the base of the triangle) into the formula to find the area of the triangle:

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

$36=\frac{1}{2}6h$

Now that you plugged in the area and the base into the formula to find the area of a triangle, you can solve for the height:

Multiply both sides by 2 (the reciprocal of 1/2) to get rid of the fraction

$236=\frac{1}{2}6h2$

Divide both sides by 6 to find the height

$\frac{72}{6}=\frac{6}{6}h$

Remember that is the same as

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Question

A triangle has a base that is 8 cm. and a height that is 12 cm. What is the area of this triangle?

Answer

To find the area of the triangle, we need to plug in what we know (the base and the height) into the formula to find the area of the triangle:

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

$A=\frac{1}{2}812$

We can know solve for

$A=\frac{1}{2}812$

$A=48cm.^{2}$

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Question

The area of a triangle is 12 square inches. It has a height of 4 inches. What is the triangle's base, in inches?

Answer

The area of a triangle is:

$A = \frac{1}{2}b\times h$

Given that the area is 12 and the base is 4, this gives us:

$12= \frac{1}{2}(4)\times h$

This reduces to:

$12= 2\times h$

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Question

A triangle has a base of 8 inches and a height of 4 inches. What is the area in square inches?

Answer

The area of a triangle can be calculated using this formula:

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

When inputting the base and height information, the equation looks like this:

$Area=\frac{8\cdot 4}{2}$

$Area=\frac{32}{2}$

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Question

A triangle has a base of 7 and a height of 4. What is the area of the triangle?

Answer

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

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

Plugging in the appropriate values for this equation gives us:

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

This reduces to:

$Area =\frac{28}2{}=14$

This is equal to 14, the correct answer.

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Question

A triangle has a height of 6 inches and a base of 3 inches. What is the area, in square inches?

Answer

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

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

Here, the base is 3 inches and the height is 6 inches. When plugging this information into the formula, we get:

$Area =\frac{3\times 6}{2}$

$Area=\frac{18}{2}$

This fraction reduces to 9, the correct answer.

$\frac{18}{2}=\frac{18\div2}{2\div2}=\frac{9}{1}=9$

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Question

If a triangle has a base of 1 foot, and a height of half a foot, what is the area in square inches?

Answer

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

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

Since we are looking for the area in inches, we must convert the base and height to inches, from feet.

$1\text{ft}=12\text{in}=base$

$\frac{1}{2}\text{ft}=6\text{in}=height$

This gives us a base of 6 inches and a height of 12 inches. Plug these values into the area equation and solve.

$Area =\frac{6\cdot 12}{2}$

$Area =\frac{72}{2}$

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Question

What is the area of a triangle for which the base is 9 inches and the height is 12 inches?

Answer

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

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

Given that the base is 9 inches and the height is 12 inches, plugging these numbers into the equation gives us the following:

$Area =\frac{9\cdot 12}{2}$

$Area = \frac{108}{2}$

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Question

If a triangle has a height of 2 inches and a base that is 3 times as long, what is the area?

Answer

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

Given that the height is 2 inches, and the base is 3 times that of the height, the base is 6 inches.

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

$Area =\frac{6\cdot 2}2{}$

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Question

If the area of a triangle is 15 feet and the height is 5 feet, what is the length of the base?

Answer

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

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

$15=\frac{5\cdot base}{2}$

Each side of the equation should be multiplied by 2.

$30=5\cdot base$

Each side should be divided by 5.

Therefore, the base has a value of 6.

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Question

Find the area of a triangle whose base is and height is .

Answer

To solve, simply use the formula for the area of a triangle. Thus,

$A=\frac{1}{2}Bh=\frac{1}{2}56=15$

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Question

How much area does a triangular garden have with a base of and a height of ?

Answer

The area of a triangle is

$\frac{1}{2}baseheight$

so given that the base is 5 and the height is 6, the area equation becomes,

and

$\frac{1}{2}*30=15$ .

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Question

If you have a right triangle with a height of 6 inches, a base of 8 inches, and a hypotenuse of 10 inches, what is its area?

Answer

If you have a right triangle with a height of 6 inches, a base of 8 inches, and a hypotenuse of 10 inches, what is its area?

To find area of a triangle, we use

$A_{triangle}=\frac{1}{2}bh$

So, plug in our base and height measurements to get our answer:

$A_{triangle}=\frac{1}{2}8in6in=24 in^2$

Coincidentally, the same as our perimeter

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Question

If the formula for the area of a triangle is

$A=\frac{1}{2} \times base \times height$ ,

what is the area of this triangle?

Answer

Using the formula:

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

where

$A=\frac{1}{2}(8\times 5)$

Since $8\times 5=40$ the equation becomes

$A=\frac{1}{2}(40)=\frac{40}{2}=\frac{20\cdot 2}{2}=20$

$A= 20cm^{2}$

Note: Answer will always be represented with the measurement to the second power when calculating the area of a triangle.

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Question

Find the area of a triangle with a height of 12in and a base that is half the height.

Answer

The formula to find the area of a triangle is

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

We know the height of the triangle is 12in. We know the base is half the height, so the base is 6in. Now, we can substitute. We get

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{in} \cdot 12\text{in}$

$\text{area of triangle} = \frac{1}{2} \cdot72\text{in}^2$

$\text{area of triangle} = 36\text{in}^2$

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Question

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

Answer

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

First multiply the base and the height together:

Then divide the product by two:

$\frac{x^2 + 2x}{2}$

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