How to find the area of a right triangle - Geometry

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Question

Given that:

A = 6 cm

B = 10 cm

What is the area of the right trianlge ABC?

Answer

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)(base)(height)$

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

$A_{\Delta }=(1/2)106 = 12 cm^{2}$

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Question

Given that:

A = 3 cm

B = 4 cm

C = 5 cm

What is the area of the right triangle ABC?

Answer

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)(base)(height)$

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

$A_{\Delta }=(1/2)43 = 6 cm^{2}$

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Question

Given that:

A = 10 cm

B = 20 cm

What is the area of the right triangle ABC?

Answer

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)(base)(height)$

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

$A_{\Delta }=(1/2)2010 = 100 cm^{2}$

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Question

Find the area of a right triangle with base 4 and height 5.

Answer

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

$A=\frac{1}{2}Bh=\frac{1}{2}45=10$

If the formula escapes you, simply remember that two equivalent triangles put together equal a rectangle. So, the area of a triangle must be half the area of a rectangle.

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Question

Find the area.

Answer

Recall how to find the area of a triangle:

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

Since this is a right triangle, the base and the height are the two leg lengths given.

$\text{Area}=\frac{20\times14}{2}=140$

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Question

Find the area.

Answer

Recall how to find the area of a triangle:

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

Since this is a right triangle, the base and the height are the two leg lengths given.

$\text{Area}=\frac{9\times5}{2}=\frac{45}{2}=22.5$

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Question

Find the area.

Answer

Recall how to find the area of a triangle:

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

Since this is a right triangle, the base and the height are the two leg lengths given.

$\text{Area}=\frac{2.5\times0.25}{2}=0.3125$

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Question

Find the area.

Answer

Recall how to find the area of a triangle:

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

Since this is a right triangle, the base and the height are the two leg lengths given.

$\text{Area}=\frac{20\times5}{2}=100$

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Question

Find the area.

Answer

Recall how to find the area of a triangle:

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

Since this is a right triangle, the base and the height are the two leg lengths given.

$\text{Area}=\frac{2.5\times1.75}{2}=2.1875$

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Question

Given:

A = 3 cm

B = 7 cm

What is the area of the triangle?

Answer

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)(base)(height)$

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

$A_{\Delta }=(1/2)37 = 10.5 cm^{2}$

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Question

The ratio for the side lengths of a right triangle is 3:4:5. If the perimeter is 48, what is the area of the triangle?

Answer

We can model the side lengths of the triangle as 3x, 4x, and 5x. We know that perimeter is 3x+4x+5x=48, which implies that x=4. This tells us that the legs of the right triangle are 3x=12 and 4x=16, therefore the area is A=1/2 bh=(1/2)(12)(16)=96.

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Question

A right triangle has a total perimeter of 12, and the length of its hypotenuse is 5. What is the area of this triangle?

Answer

The area of a triangle is denoted by the equation 1/2 b x h.

b stands for the length of the base, and h stands for the height.

Here we are told that the perimeter (total length of all three sides) is 12, and the hypotenuse (the side that is neither the height nor the base) is 5 units long.

So, 12-5 = 7 for the total perimeter of the base and height.

7 does not divide cleanly by two, but it does break down into 3 and 4,

and 1/2 (3x4) yields 6.

Another way to solve this would be if you recall your rules for right triangles, one of the very basic ones is the 3,4,5 triangle, which is exactly what we have here

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Question

The length of one leg of an equilateral triangle is 6. What is the area of the triangle?

Answer

$A=\frac{1}{2}(B)(H)$

The base is equal to 6.

The height of an quilateral triangle is equal to $\frac{B\sqrt{3}}{2}$ , where is the length of the base.

$A=\frac{1}{2}(6)(\frac{6\sqrt{3}}{2})=\frac{1}{2}(6)(3\sqrt{3})=9\sqrt{3}$

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Question

Given:

A = 3 cm

B = 4 cm

What is the area of the right triangle ABC?

Answer

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)(base)(height)$

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

$A_{\Delta }=(1/2)34 = 6 cm^{2}$

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Question

Given:

A = 4 cm

B = 6 cm

What is the area of the right triangle ABC?

Answer

The area of a triangle is given by the equation:

$A_{\Delta } = (1/2)(base)(height)$

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

$A_{\Delta }=(1/2)46 = 12 cm^{2}$

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Question

An equilateral triangle has a side of .

What is the area of the triangle?

Answer

An equilateral triangle has three congruent sides. The area of a triangle is given by $A = \frac{1}{2}bh$ where is the base and is the height.

The equilateral triangle can be broken into two right triangles, where the legs are and and the hypotenuses is .

Using the Pythagorean Theorem we get $4^{2}=2^{2} + x^{2}$ or $x=2\sqrt{3}$ and the area is $A = \frac{1}{2}bh= \frac{1}{2}(4)(2\sqrt{3}) = 4\sqrt{3}$

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Question

The length of the legs of the triangle below (not to scale) are as follows:

cm

cm

What is the area of the triangle?

Answer

The formula for the area of a triangle is

$\frac{1}{2}bh$

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

For the triangle shown, side is the base and side is the height.

Therefore, the area is equal to

$\frac{1}{2}(7)(12)=42$

or, based on the units given, 42 square centimeters

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Question

The hypotenuse of a $30^{\circ }-60^{\circ }-90^{\circ }$ triangle measures eight inches. What is the area of this triangle (radical form, if applicable)?

Answer

In a $30^{\circ }-60^{\circ }-90^{\circ }$ , the shorter leg is half as long as the hypotenuse, and the longer leg is $\sqrt{3}$ times the length of the shorter. Since the hypotenuse is 8, the shorter leg is 4, and the longer leg is $4\sqrt{3}$ , making the area:

$A = \frac{1}{2} bh = \frac{1}{2} \cdot 4 \cdot 4\sqrt{3} = 8\sqrt{3}$

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Question

$What;is;the;area;of;\Delta GHJ?$

Answer

$Area ;\Delta= \frac{1}{2}(base)(height)$

$\Delta GHF=\frac{1}{2}(5)(12)=\frac{1}{2}(60)=30$

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Question

$What;is;the;area;of;\Delta KLM?$

Answer

$Area ;\Delta=\frac{1}{2}(base)(height)$

$Area;\Delta KLM=\frac{1}{2}(3)(4)=\frac{1}{2}(12)=6$

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