Figure \(\PageIndex1\)

Marie has a arsenal of photos of buildings shaped like pyramids. As she looked through the photos, she wondered just how tall among the structures was. She knows the the area that the triangle shaped surface is 900 square feet. She additionally knows the the length of each side of the base of the pyramid (which is also the length of the basic of each triangular side) is 60 feet. Given the base and area that the triangles developing the pyramid, how have the right to Marie recognize the elevation of the pyramid?

In this concept, you will learn how to find the unknown dimensions of triangles given the area and another dimension.

You are watching: How to find the dimensions of a triangle

Example \(\PageIndex1\)

Earlier, girlfriend were given a problem about Marie and her picture of pyramid buildings.

Marie uncovered out the area of each triangle shaped surface is 900 square feet. She additionally knows that the size of every side of the base of the pyramid (which is additionally the size of the basic of every triangular side) is 60 feet. Marie uncovered the formula for computing the area of a triangle, and decided to use it to number out the triangle’s height.

\(A=\dfrac12bh\)

Solution

First, she should substitute the given information right into the formula.

\(900=\dfrac12(60)h\)

Next, main point one-half through 60.

\(900=30h\)

Then, resolve for the base by separating both sides by 30.

\(\beginalign* \dfrac90030&=\dfrac30h30 \\ 30 &=h\endalign*\)

The answer is 30. The height of this pyramid is 30 feet.

Example \(\PageIndex2\)

Find the absent dimension that the adhering to triangle.

The area that the triangle is 48 square feet. The basic of the triangle is 12 feet. What is the height?

Solution

Start by looking at the formula because that finding the area of a triangle.

\(A=\dfrac12bh\)

First, to fill in the given information.

\(48=\dfrac12(12)h\)

Next, multiply one-half by 12.

\(48=6h\)

Then, resolve for the basic by splitting 48 by 6.

\(\beginalign* \dfrac486&=\dfrac6h6 \\ 8 &=h\endalign*\)

The prize is 8. The height of this triangle is 8 feet.

Example \(\PageIndex3\)

A triangle has actually an area that 42 sq. Ft. If the base is 12 feet, what is the measure up of the height?

Solution

To number this out, begin by looking at the formula because that finding the area that a triangle.

\(A=\dfrac12bh\)

First, instead of the offered information into the formula.

\(42=\dfrac12 (12)h\)

Next, main point one-half by 12.

\(42=6h\)

Then, solve for the basic by dividing both sides by 6.

\(\beginalign* \dfrac426 &=6h \\ 7&=6h\endalign*\)

The price is 7. The elevation of this triangle is 7 feet.

Example \(\PageIndex4\)

A triangle has actually an area of 16 sq. Cm. If the height of the triangle is 4 cm, what is the measure of the base?

Solution

To number this out, begin by looking at the formula for finding the area of a triangle.

\(A=\dfrac12bh\)

First, instead of the offered information into the formula.

\(16=\dfrac12b(4)\)

Next, multiply one-half by 4.

\(16=2b\)

Then, deal with for the basic by dividing both sides by 2.

\(\beginalign* \dfrac162 &=\dfrac2b2 \\ 8&=b \endalign*\)

The prize is 8. The height of this triangle is 8 cm.

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## Review

Find the missing dimension given the area and either the basic or height of a triangle.

Area = 15 sq. In, basic = 10 in, what is the height? Area = 40 sq. In, base = 20 in, what is the height? Area = 24 sq. Ft, base = 8 ft, what is the height? Area = 16 sq. M, base = 8 m, what is the height? Area = 25 sq. In, elevation = 5 in, what is the base? Area = 36 sq. Ft, elevation = 6 ft, what is the base? Area = 54 sq. Cm, elevation = 9 cm, what is the base? Area = 80 sq. Meters, base = 16 meters, what is the height? Area = 75 sq. Meters, base = 10 meters, what is the height? Area = 90 sq. Meters, basic = 30 meters, what is the height? Area = 180 sq. Meters, basic = 10 meters, what is the height? Area = 90 sq. Meters, basic = 15 meters, what is the height? Area = 120 sq. Meters, basic = 60 meters, what is the height? Area = 150 sq. Meters, base = 50 meters, what is the height? Area = 280 sq. Meters, base = 140 meters, what is the height?