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What is the area of the triangle XYZ to the nearest TENTH of a square ft?

What is the area of the triangle XYZ to the nearest TENTH of a square ft?-example-1
User Turankonan
by
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1 Answer

9 votes

Answer:

55.4 ft²

Explanation:

The special triangle with angles 30°-60°-90° has side lengths in the ratios ...

1 : √3 : 2

The area of the triangle can be found using the area formula ...

A = 1/2bh

where b is the base and h is the perpendicular height.

__

sides

The longest side is given as 16 ft. This corresponds to "2" in the ratio, so the other two sides have lengths ...

8 ft, 8√3 ft

__

area

These area the perpendicular sides of the triangle so, work well to find the area.

A = 1/2bh

A = 1/2(8√3 ft)(8 ft) = 32√3 ft²

A ≈ 55.4 ft²

The area of the triangle is about 55.4 square feet.

User Joseph Astrahan
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