what is the area of triangle fgh? round your answer to the nearest tenth of a square centimeter.

The area of a triangle is ever half the production of the tiptop and base.

$ Area = \frac{i}{2} (base \cdot top) $

So which side is the base?

Reply

Whatsoever side of the triangle can be a base. All that matters is that the base and the peak must be perpendicular.

Any side can be a base of operations, but every base has only one superlative. The height is the line from the opposite vertex and perpendicular to the base. The illustration below shows how whatsoever leg of the triangle can exist a base and the height always extends from the vertex of the opposite side and is perpendicular to the base of operations. Play around with our applet to see how the area of a triangle can be computed from whatever base/elevation pairing.

The picture below shows you that the acme can actually extend exterior of the triangle. So technically the summit does non necessarily intersect with the base.

Derivation of the Area of a Triangle from Rectangle

Example ane

What is the area of the triangle pictured below?

Use the formula higher up.

$$ A = \frac{1}{2} (base \cdot height) \\ A = \frac{1}{2} (10 \cdot 3) \\ = \frac{one}{two} (xxx) \\ = \frac{30}{2} = fifteen $$

Exercise Problems

Observe the area of each triangle below. Round each answer to the nearest tenth of a unit of measurement.

Problem 1

What is the expanse of the triangle in the post-obit picture?

To find the surface area of the triangle on the left, substitute the base and the acme into the formula for area.

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{one}{2} (three \cdot 3) \\ = \frac{i}{ii} (9) \\ =\frac{ix}{2} \\ = four.5 \text{ inches squared} $$

Problem 2

Calculate the area of the triangle pictured below.

To discover the area of the triangle on the left, substitute the base and the pinnacle into the formula for area.

$$ Area = \frac{i}{two} (base \cdot height) \\ =\frac{1}{2} (24 \cdot 27.6) \\ = 331.2 \text{ inches squared} $$

Problem three

Calculate the area of the triangle pictured beneath.

To notice the area of the triangle on the left, substitute the base and the peak into the formula for area.

$$ Expanse = \frac{one}{2} (base of operations \cdot top) \\ =\frac{1}{2} (12 \cdot 2.5) \\ = 15 \text{ inches squared} $$

Problem 4

Calculate the area of the triangle pictured below.

To notice the expanse of the triangle on the left, substitute the base and the height into the formula for area.

$$ Area = \frac{one}{ii} (base \cdot elevation) \\ =\frac{1}{2} (12 \cdot iii.ix) \\ = 23.4 \text{ inches squared} $$

Trouble 5

Calculate the area of the triangle pictured beneath.

To find the area of the triangle on the left, substitute the base and the peak into the formula for expanse.

$$ Area = \frac{one}{ii} (base of operations \cdot elevation) \\ =\frac{1}{ii} (14 \cdot 4) \\ = 28 \text{ inches squared} $$

Problem 6

What is the expanse of the following triangle?

This problems involves i pocket-sized twist. Y'all must decide which of the 3 bases to use. Just call back that base and pinnacle are perpendicular. Therefore, the base is '11' since it is perpendicular to the height of 13.4.

To find the area of the triangle on the left, substitute the base and the height into the formula for area.

$$ Area = \frac{1}{ii} (base \cdot height) \\ =\frac{1}{2} (xi \cdot thirteen.iv) \\ = 73.seven \text{ inches squared} $$

Problem 7

What is the expanse of the post-obit triangle?

This problems involves ane modest twist. You lot must determine which of the 3 bases to use. Just remember that base and height are perpendicular. Therefore, the base is '12' since information technology is perpendicular to the height of 5.9.

To find the surface area of the triangle on the left, substitute the base and the height into the formula for area.

$$ Expanse = \frac{1}{2} (base of operations \cdot elevation) \\ =\frac{1}{two} (12 \cdot five.9) \\ = 35.iv \text{ inches squared} $$

Trouble 8

What is the area of the following triangle?

Like the final problem, you must decide which of the 3 bases to employ. Just remember that base of operations and height are perpendicular. Therefore, the base is 'four' since it is perpendicular to the pinnacle of 17.7.

To find the area of the triangle on the left, substitute the base and the height into the formula for area.

$$ Area = \frac{1}{2} (base of operations \cdot height) \\ =\frac{1}{2} (4 \cdot 17.seven) \\ = 35.4 \text{ inches squared} $$

Problem 9

What is the area of the following triangle?

Over again, you must decide which of the 3 bases to use. Just remember that base and height are perpendicular. Therefore, the base is '22' since it is perpendicular to the height of 26.8.

To find the area of the triangle on the left, substitute the base and the height into the formula for area.

$$ Area = \frac{i}{2} (base \cdot pinnacle) \\ =\frac{one}{ii} (22 \cdot 26.eight) \\ = 294.8 \text{ inches squared} $$

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Source: https://www.mathwarehouse.com/geometry/triangles/area/index.php

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