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Basic Geometry : Triangles

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Example Questions

Example Question #81 : How To Find The Area Of A Right Triangle

The diameter of the circle is , find the area of the shaded region.

Possible Answers:

13.38

9.98

12.41

10.99

Correct answer:

13.38

Explanation:

To find the area of the shaded region, we will first need to find the area of the right triangle and the area of the circle.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi\times\text{radius}^2$

Now, recall how to find the length of the radius from the length of the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

Substitute in the given diameter to find the radius.

$\text{Radius}=\frac{9}{2}$

Now, substitute in the radius to find the area of the circle.

$\text{Area of Circle}=\pi\times\left( \frac{9}{2}\right)^2$

$\text{Area of Circle}=\frac{81}{4}\pi$

Next, recall how to find the area of a right triangle.

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

Substitute in the given base and height to find the area.

$\text{Area of Triangle}=\frac{11 \times 14}{2}$

$\text{Area of Triangle}=77$

We can now find the area of the shaded region:

$\text{Area of Shaded Region}=\text{Area of Triangle}-\text{Area of Circle}$

$\text{Area of Shaded Region}=77-\frac{81}{4}\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=13.38$

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Example Question #82 : How To Find The Area Of A Right Triangle

The diameter of the circle is 2.2 , find the area of the shaded region.

Possible Answers:

17.78

15.98

16.20

14.28

Correct answer:

16.20

Explanation:

To find the area of the shaded region, we will first need to find the area of the right triangle and the area of the circle.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi\times\text{radius}^2$

Now, recall how to find the length of the radius from the length of the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

Substitute in the given diameter to find the radius.

$\text{Radius}=\frac{2.2}{2}$

$\text{Radius}=1.1$

Now, substitute in the radius to find the area of the circle.

$\text{Area of Circle}=\pi\times 1.1^2$

$\text{Area of Circle}=1.21\pi$

Next, recall how to find the area of a right triangle.

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

Substitute in the given base and height to find the area.

$\text{Area of Triangle}=\frac{4 \times 10}{2}$

$\text{Area of Triangle}=20$

We can now find the area of the shaded region:

$\text{Area of Shaded Region}=\text{Area of Triangle}-\text{Area of Circle}$

$\text{Area of Shaded Region}=20-1.21\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=16.20$

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Example Question #84 : How To Find The Area Of A Right Triangle

The diameter of the circle is , find the area of the shaded region.

Possible Answers:

89.89

93.44

90.90

91.28

Correct answer:

90.90

Explanation:

To find the area of the shaded region, we will first need to find the area of the right triangle and the area of the circle.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi\times\text{radius}^2$

Now, recall how to find the length of the radius from the length of the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

Substitute in the given diameter to find the radius.

$\text{Radius}=\frac{12}{2}$

$\text{Radius}=6$

Now, substitute in the radius to find the area of the circle.

$\text{Area of Circle}=\pi\times 6^2$

$\text{Area of Circle}=36\pi$

Next, recall how to find the area of a right triangle.

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

Substitute in the given base and height to find the area.

$\text{Area of Triangle}=\frac{17 \times 24}{2}$

$\text{Area of Triangle}=204$

We can now find the area of the shaded region:

$\text{Area of Shaded Region}=\text{Area of Triangle}-\text{Area of Circle}$

$\text{Area of Shaded Region}=204-36\pi$

Solve and round to two decimal places.

$\text{Area of Shaded Region}=90.90$

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Example Question #481 : Triangles

A triangle has a height of 5 inches and a base of 10 inches. What is the area of this triangle?

Possible Answers:

None of these.

A=25in^2

A=15in^2

A=65in^2

A=30in^2

Correct answer:

A=25in^2

Explanation:

The area of a right triangle can be found by A=.5bh .

$A=.5bh=.5(10)(5)=\mathbf{25in^2}$

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Example Question #86 : How To Find The Area Of A Right Triangle

Prblem 6 basic geometry

Triangle ABC has the given side lengths. Find the area of triangle ABC.

Possible Answers:

$100\ inches^2$

$182\ inches^2$

$121\ inches^2$

$91\ inches^2$

$89\ inches^2$

Correct answer:

$91\ inches^2$

Explanation:

Imagine a right triangle as a square cut in half at a diagonal angle.

When figuring out the area, you figure it out the same way as finding the area of a square, but after multiplying length x width, divide the answer by 2.

$14 \cdot 13 = 182inches^2$

182/2=91 inches^2

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Example Question #87 : How To Find The Area Of A Right Triangle

Find the area, , of a right triangle XYZ whose sides are X=12 , Y=5 , Z=13 .

Possible Answers:

A=35

A=50

A=30

A=40

Correct answer:

A=30

Explanation:

The formula for the area of a right triangle is

$A=\frac{1}{2}XY$ .

Plugging in the values given,

$A=\frac{1}{2}*5*12=30$ .

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Example Question #84 : How To Find The Area Of A Right Triangle

Shape area right triangle

In the right triangle shown here, a=5 and b=12 . What is its area in square units?

Possible Answers:

Correct answer:

Explanation:

The area of a right triangle is given by $A=\frac{bh}{2}$ , where represents the length of the triangle's base and represents the length of the triangle's height. The base and the height of the triangle given in the problem are and units long, respectively. Hence, the area of the triangle can be calculated as follows:

$A=\frac{bh}{2}= \frac{(12)(5)}{2} = 30$ .

Hence, the area of a right triangle with base length units and height units is square units.

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Example Question #1 : How To Find If Right Triangles Are Congruent

Are the two right triangles congruent?

Possible Answers:

Yes, by AAA

Yes, by HL

Yes, by AAS

Yes, by AAA

No, they are not congruent

Correct answer:

Yes, by HL

Explanation:

Right triangles are congruent if both the hypotenuse and one leg are the same length. These triangles are congruent by HL, or hypotenuse-leg.

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Example Question #1 : How To Find If Right Triangles Are Congruent

Which of the following is not sufficient to show that two right triangles are congruent?

Possible Answers:

All the sides are congruent.

All the angles are congruent.

Both legs are congruent.

The hypotenuse and one leg are congruent.

Correct answer:

All the angles are congruent.

Explanation:

Two right triangles can have all the same angles and not be congruent, merely scaled larger or smaller. If all the side lengths are multiplied by the same number, the angles will remain unchanged, but the triangles will not be congruent.

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Example Question #1 : How To Find If Right Triangles Are Congruent

Which of the following pieces of information would not allow the conclusion that

$\bigtriangleup ABD\cong \bigtriangleup CBD$

Possible Answers:

$m\angle ABC =100^o$

$\angle BAC\cong \angle BCA$

AB=10

AC=16

$\overrightarrow{BD}$ bisects $\angle ABC$

Correct answer:

$m\angle ABC =100^o$

Explanation:

To determine the answer choice that does not lead to congruence, we should simply use process of elimination.

If AC=16 , then subtracting tells us that DC=8 .; therefore $\overline{AD}\cong \overline{DC}$ . Given the fact that reflexively $\overline{BD}\cong\overline{BD}$ and that both $\angle BDA$ and $\angle BDC$ are both right angles and thus congruent, we can establish congruence by way of Side-Angle-Side.

Similarly, if AB=10 , then $\overline{AB}\cong \overline{BC}$ , and given the other information we determined with our last choice, we can establish conguence by way of Hypotenuse-Leg.

If $\angle BAC\cong \angle BCA$ , given what we already know we can establish congruence by Angle-Angle-Side

Finally, if $\overrightarrow{BD}$ is an angle bisector, then our two halves are congruent. $\angle ABD\cong \angle CBD$ . Given what we know, we can establish congruence by Angle-Side-Angle

The only remaining choice is the case where $m\angle ABC=100^o$ . This does not tell us how the two parts of this angle are related, we lack enough information for congruence.

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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #81 : How To Find The Area Of A Right Triangle

Example Question #82 : How To Find The Area Of A Right Triangle

Example Question #84 : How To Find The Area Of A Right Triangle

Example Question #481 : Triangles

Example Question #86 : How To Find The Area Of A Right Triangle

Example Question #87 : How To Find The Area Of A Right Triangle

Example Question #84 : How To Find The Area Of A Right Triangle

Example Question #1 : How To Find If Right Triangles Are Congruent

Example Question #1 : How To Find If Right Triangles Are Congruent

Example Question #1 : How To Find If Right Triangles Are Congruent

All Basic Geometry Resources

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