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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #6 : How To Find The Area Of A Right Triangle

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)?

Possible Answers:

$8\sqrt{2} \; \textrm{in}^{2}$

$16 \; \textrm{in}^{2}$

It is impossible to tell from the information given.

$8\; \textrm{{in}}^{2}$

$8\sqrt{3} \; \textrm{in}^{2}$

Correct answer:

$8\sqrt{3} \; \textrm{in}^{2}$

Explanation:

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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Example Question #3 : How To Find The Area Of A Right Triangle

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

Possible Answers:

Correct answer:

Explanation:

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

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

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Example Question #1391 : Plane Geometry

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

Possible Answers:

Correct answer:

Explanation:

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

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

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Example Question #411 : Triangles

What is the area of a right triangle with a height of 5 inches and a base of 3 inches?

Possible Answers:

7.5

3.5

Correct answer:

7.5

Explanation:

To find the area of a triangle, multiply the base by the height, then divide by 2.

$3\cdot 5=15$

15/2=7.5

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Example Question #1391 : Plane Geometry

Find the area of ONE of the triangles formed by the diagonal.

Possible Answers:

192

Correct answer:

Explanation:

To find the area of a right triangle, use the formula $A = \frac{1}{2}bh$ , where is the area of the triangle, is the length of the triangle's base, and is the triangle's height.

$A = \frac{1}{2}(8)(12)$

A= 48

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Example Question #1 : How To Find The Area Of A Right Triangle

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

Possible Answers:

Correct answer:

Explanation:

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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Example Question #1 : Triangles

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?

Possible Answers:

108

240

Correct answer:

Explanation:

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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Example Question #1 : How To Find The Area Of A Right Triangle

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

Possible Answers:

$9\sqrt{3}$

Correct answer:

$9\sqrt{3}$

Explanation:

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

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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Example Question #11 : Right Triangles

Find the area of the following right triangle to the nearest integer Finding_area_of_right_triangle

Note: The triangle is not necessarily to scale

Possible Answers:

None of the other answers

104

Correct answer:

Explanation:

The equation used to find the area of a right triangle is: $A = \frac{1}{2}b\cdot h$ where A is the area, b is the base, and h is the height of the triangle. In this question, we are given the height, so we need to figure out the base in order to find the area. Since we know both the height and hypotenuse of the triangle, the quickest way to finding the base is using the pythagorean theorem, $a^{2}+b^{2}=c^{2}$ . a = the height, b = the base, and c = the hypotenuse.

Using the given information, we can write $8^{2} + b^{2} = 13^{2}$ . Solving for b, we get $b^{2} = 105$ or $b \approx 10.25$ . Now that we have both the base and height, we can solve the original equation for the area of the triangle. $A = \frac{1}{2}\cdot10.25\cdot8 = 40.99\approx41$

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Example Question #221 : Right Triangles

Find the area of this right triangle:

Right triangle perim 2

Possible Answers:

$\small \sqrt{66}$

$\small \frac{1}{2}\sqrt{132}$

$\small 3.5\sqrt{33}$

$\small 2\sqrt{65}$

$\small 2\sqrt{33}$

Correct answer:

$\small 2\sqrt{33}$

Explanation:

The area of a triangle is $\small \frac{1}{2}(base)(height)$ . For a right triangle, we can use the two legs as the base and the height regardless of orientation. Right now we only know one of the legs, and we can solve for the other using Pythagorean Theorem:

$\small \small 4^2 + x^2 = 7^2$

$\small 16 + x^2 = 49$ subtract 16 from both sides

$\small x^2 = 33$

$\small x = \sqrt{33}$ we can see that all of the answers are in radical form, so we do not have to simplify this to a crazy decimal.

Now we have our "base" and "height" and we can plug them into the formula to find the area:

$\small \frac{1}{2}*4*\sqrt{33}$ half of 4 is 2, so our answer is $\small 2\sqrt{33}$ , which we can't simplify any more.

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #6 : How To Find The Area Of A Right Triangle

Example Question #3 : How To Find The Area Of A Right Triangle

Example Question #1391 : Plane Geometry

Example Question #411 : Triangles

Example Question #1391 : Plane Geometry

Example Question #1 : How To Find The Area Of A Right Triangle

Example Question #1 : Triangles

Example Question #1 : How To Find The Area Of A Right Triangle

Example Question #11 : Right Triangles

Example Question #221 : Right Triangles

All Basic Geometry Resources

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