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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : 45/45/90 Right Isosceles Triangles

Isosceles

An isosceles right triangle has a hypotenuse of $h=18\sqrt{2} in$ . Find its area.

Possible Answers:

Not enough information to solve

$5.4ft^{2}$

$4.5ft^{2}$

$1.125ft^{2}$

$2.115ft^{2}$

Correct answer:

$1.125ft^{2}$

Explanation:

In order to calculate the triangle's area, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as $45^{\circ}-45^{\circ}-90^{\circ}$ triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.

$x=\frac{h}{\sqrt{2}}$

$x=\frac{18\sqrt{2}in}{\sqrt{2}}$

x=18in

Now we can calculate the area using the formula

$A=\frac{1}{2}bh$

$A=\frac{1}{2}*18in*18in$

$A=162in^{2}$

Now, convert to feet.

$\rightarrow \frac{162 in^{2}}{1}*\frac{1ft}{12in}*\frac{1ft}{12in}=1.125ft^{2}$

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Example Question #2 : 45/45/90 Right Isosceles Triangles

The base of a right isosceles triangle is 8 inches. The hypotenuse is not the base. What is the area of the triangle in inches?

Possible Answers:

128

Correct answer:

Explanation:

To find the area of a triangle, multiply the base by the height, then divide by 2. Since the short legs of an isosceles triangle are the same length, we need to know only one to know the other. Since, a short side serves as the base of the triangle, the other short side tells us the height.

$(8\cdot 8)/2=32$

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Example Question #4 : 45/45/90 Right Isosceles Triangles

Isosceles

The hypotenuse of an isosceles right triangle has a measure of h=8cm . Find its perimeter.

Possible Answers:

19.31cm

Not enough information to solve

13.92cm

12.32cm

20.22cm

Correct answer:

19.31cm

Explanation:

In order to calculate the triangle's perimeter, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as $45^{\circ}-45^{\circ}-90^{\circ}$ triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.

$x=\frac{h}{\sqrt{2}}$

$x=\frac{8}{\sqrt{2}}$

$x=4\sqrt{2}$

Now we can calculate the perimeter by doubling and adding .

P=2x+h

$P=(2*4\sqrt{2})+8cm$

P=19.31cm

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Example Question #3 : 45/45/90 Right Isosceles Triangles

Isosceles

The side lengths of an isoceles right triangle measure x=14cm . Find its perimeter.

Possible Answers:

42cm

48.70cm

47.80cm

40.87cm

Not enough information to solve

Correct answer:

47.80cm

Explanation:

An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as $45^{\circ}-45^{\circ}-90^{\circ}$ triangles and their side lenghts follow a specific pattern that states you can calculate the length of the hypotenuse of an isoceles triangle by multiplying the length of one of the legs by the square root of 2.

$h=x\sqrt{2}$

$h=14cm\sqrt{2}$

h=19.80cm

Now we can calculate the perimeter by doubling and adding .

P=2x+h

P=(14cm*2)+19.80cm

P=47.8cm

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Example Question #2 : 45/45/90 Right Isosceles Triangles

A triangle has two angles equal to $45^\circ$ and two sides equal to . What is the perimeter of this triangle?

Possible Answers:

$\frac{48\sqrt{2}}{2}$

$16+8\sqrt{2}$

$24\sqrt{2}$

Correct answer:

$16+8\sqrt{2}$

Explanation:

When a triangle has two angles equal to $45^\circ$ , it must be a $45^\circ:45^\circ:90^\circ$ isosceles right triangle.

The pattern for the sides of a $45^\circ:45^\circ:90^\circ$ is $x:x:x\sqrt{2}$ .

Since two sides are equal to , this triangle will have sides of $8:8:8\sqrt{2}$ .

Add them all together to get $16+8\sqrt{2}$ .

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Example Question #1 : 45/45/90 Right Isosceles Triangles

An isosceles triangle has a base of 6 and a height of 4. What is the perimeter of the triangle?

Possible Answers:

None of these

Correct answer:

Explanation:

An isosceles triangle is basically two right triangles stuck together. The isosceles triangle has a base of 6, which means that from the midpoint of the base to one of the angles, the length is 3. Now, you have a right triangle with a base of 3 and a height of 4. The hypotenuse of this right triangle, which is one of the two congruent sides of the isosceles triangle, is 5 units long (according to the Pythagorean Theorem).

The total perimeter will be the length of the base (6) plus the length of the hypotenuse of each right triangle (5).

5 + 5 + 6 = 16

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Example Question #5 : 45/45/90 Right Isosceles Triangles

What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?

Possible Answers:

100

100√2

200√2

50√2

Correct answer:

100

Explanation:

Square_part1

Square_part2

Square_part3

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Example Question #21 : Triangles

Isosceles

An isosceles triangle has a hypotenuse of h=7in . Find the length of its sides, .

Possible Answers:

Not enough information to solve

7in

5.94in

4.95in

2.64in

Correct answer:

4.95in

Explanation:

An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as $45^{\circ}-45^{\circ}-90^{\circ}$ triangles and their side lengths follow a specific pattern that states you can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2

$x=\frac{h}{\sqrt{2}}$

$x=\frac{7in}{\sqrt{2}}$

$\rightarrow 4.95in$

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Example Question #31 : Triangles

Isosceles

The measure of the sides of this isosceles right triangle are $x=3\sqrt{2}$ . Find the measure of its hypotenuse, .

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

$h=x\sqrt{2}$

$h=3\sqrt{2}*\sqrt{2}$

h=3*2

$\rightarrow6$

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Example Question #1 : How To Find The Volume Of A Cylinder In Pre Algebra

What is the volume of a cylinder with a circular side with a radius of and a length of ?

Possible Answers:

$400\pi$

$72\pi$

$144\pi$

$432\pi$

Correct answer:

$432\pi$

Explanation:

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is

In this example the length is and the radius is so our equation will look like this $Volume=\pi(6^{2})(12)$

We then square the to get .

Then perform multiplication to get $432\pi$ .

The answer is $432\pi$ .

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : 45/45/90 Right Isosceles Triangles

Example Question #2 : 45/45/90 Right Isosceles Triangles

Example Question #4 : 45/45/90 Right Isosceles Triangles

Example Question #3 : 45/45/90 Right Isosceles Triangles

Example Question #2 : 45/45/90 Right Isosceles Triangles

Example Question #1 : 45/45/90 Right Isosceles Triangles

Example Question #5 : 45/45/90 Right Isosceles Triangles

Example Question #21 : Triangles

Example Question #31 : Triangles

Example Question #1 : How To Find The Volume Of A Cylinder In Pre Algebra

All High School Math Resources

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