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Pre-Algebra : Geometry

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Example Questions

Example Question #4 : Perimeter Of A Triangle

Find the perimeter of the triangle above.

Note: Figure not drawn to scale.

Possible Answers:

$24\: in$ $\displaystyle 24\: in$

$72\: in$ $\displaystyle 72\: in$

$20\: in$ $\displaystyle 20\: in$

$32\: in$ $\displaystyle 32\: in$

None of these answers are correct.

Correct answer:

$24\: in$ $\displaystyle 24\: in$

Explanation:

The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: $\displaystyle 8+12+4=24$.

Because the lengths are in inches, the answer must be in inches as well.

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Example Question #64 : Perimeter

One side of an equilateral triangle is 3.5 m $\displaystyle 3.5 m$. What is the triangle's perimeter?

Possible Answers:

3.5 m $\displaystyle 3.5 m$

10.5 m $\displaystyle 10.5 m$

Not enough information given to solve.

7 m $\displaystyle 7 m$

12 m $\displaystyle 12 m$

Correct answer:

10.5 m $\displaystyle 10.5 m$

Explanation:

Equilateral triangles have $\displaystyle 3$ sides of equal length. Therefore, by knowing the length of one side, we can calculate the perimeter by multiplying that length by $\displaystyle 3$.

$3.5m \times 3 = 10.5 m$ $\displaystyle 3.5m \times 3 = 10.5 m$

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Example Question #65 : Perimeter

In equilateral triangle ABC $\displaystyle ABC$, $\overline{AB}=8$ $\displaystyle \overline{AB}=8$.

What is the perimeter of triangle $\textup{ABC}$ $\displaystyle \textup{ABC}$?

Possible Answers:

$\displaystyle 8$

$\displaystyle 24$

$\displaystyle 16$

$\displaystyle 20$

$\displaystyle 10$

Correct answer:

$\displaystyle 24$

Explanation:

Because the triangle is equilateral, all sidelengths are equal. Thus, if one is 8 they all must be 8, so 3*8=24 $\displaystyle 3*8=24$

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Example Question #4 : Perimeter Of A Triangle

For an isosceles triangle, if two of the sides are 3 and 6, which of the following is a possible perimeter?

Possible Answers:

$\displaystyle 9$

$\displaystyle 16$

$\displaystyle 10$

$\displaystyle 13$

$\displaystyle 12$

Correct answer:

$\displaystyle 12$

Explanation:

In an isosceles triangle, two of the three sides are equal to each other. The possible side lengths of the isosceles are 3-3-6 $\displaystyle 3-3-6$ or 3-6-6 $\displaystyle 3-6-6$.

The perimeter is the sum of the three sides.

$\displaystyle 3+3+6 = 12$

$\displaystyle 3+6+6 = 15$

The only possible perimeters given the two side lengths are either $\displaystyle 12$ or $\displaystyle 15$.

The correct answer is: $\displaystyle 12$

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Example Question #1 : Perimeter Of A Triangle

What is the perimeter of an equilateral triangle with a length of 5?

Possible Answers:

125 $\displaystyle 125$

$\frac{15}{2}$ $\displaystyle \frac{15}{2}$

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

$\textup{There is not enough information.}$ $\displaystyle \textup{There is not enough information.}$

$\displaystyle 15$

Correct answer:

$\displaystyle 15$

Explanation:

There are three equal sides in an equilateral triangle.

P=3s $\displaystyle P=3s$

Substitute the side length.

$P=3\times 5 =15$ $\displaystyle P=3\times 5 =15$

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Example Question #331 : Geometry

What is the perimeter of an equilateral triangle with a side of $\sqrt2$ $\displaystyle \sqrt2$?

Possible Answers:

$2\sqrt2$ $\displaystyle 2\sqrt2$

$3\sqrt2$ $\displaystyle 3\sqrt2$

$\sqrt5$ $\displaystyle \sqrt5$

$3+\sqrt2$ $\displaystyle 3+\sqrt2$

$\sqrt6$ $\displaystyle \sqrt6$

Correct answer:

$3\sqrt2$ $\displaystyle 3\sqrt2$

Explanation:

Write the formula to find the perimeter of an equilateral triangle. All three sides are equal.

P=3s $\displaystyle P=3s$

Substitute the side length.

$P=3(\sqrt2) = 3\sqrt2$ $\displaystyle P=3(\sqrt2) = 3\sqrt2$

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Example Question #12 : Perimeter Of A Triangle

If the area of an equilateral triangle is 10, and the height is 10, what must be the perimeter of the triangle?

Possible Answers:

$\displaystyle 9$

$\displaystyle 6$

$\displaystyle 30$

$\textup{There is not enough information.}$ $\displaystyle \textup{There is not enough information.}$

$\displaystyle 3$

Correct answer:

$\displaystyle 6$

Explanation:

Write area formula for a triangle.

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

Substitute the area and the height to find the length of the base.

$10=\frac{1}{2} b(10)$ $\displaystyle 10=\frac{1}{2} b(10)$

10=5b $\displaystyle 10=5b$

b=2 $\displaystyle b=2$

The base, or the length one side of the triangle, is two.

An equilateral triangle has three equal sides. Multiply the base by three to find the perimeter.

The answer is: $\displaystyle 6$

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Example Question #332 : Geometry

What is the perimeter of an isosceles triangle with a base length of x-2 $\displaystyle x-2$?

Possible Answers:

$\displaystyle 6x$

3x-6 $\displaystyle 3x-6$

3x-2 $\displaystyle 3x-2$

$\textup{There is not enough information.}$ $\displaystyle \textup{There is not enough information.}$

3x+6 $\displaystyle 3x+6$

Correct answer:

$\textup{There is not enough information.}$ $\displaystyle \textup{There is not enough information.}$

Explanation:

For an isosceles triangle, two of the side legs are equal. It is necessary to know two of the three sides in order to sum the lengths. The problem only gave us the length of the base.

There is not enough information to solve this question since the length of the other leg is unknown.

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Example Question #333 : Geometry

Find the perimeter of an isosceles triangle with a base of 4 inches and side length of 10 inches.

Possible Answers:

$\displaystyle 14 inches$

$\displaystyle 28 inches$

$\displaystyle 16 inches$

$\displaystyle 24 inches$

$\displaystyle 40 inches$

Correct answer:

$\displaystyle 24 inches$

Explanation:

An isosceles triangle has two sides that have the same length. If the base is 4 and one of the sides is 10, then the other side is also 10.

$\displaystyle 10 + 10 + 4 = 24inches$

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Example Question #334 : Geometry

An equilateral triangle measures $\displaystyle 9$ inches along its side. What is the area of the triangle?

Possible Answers:

$\displaystyle 25$ square inches

$\displaystyle 21$ square inches

$\displaystyle 22$ square inches

$\displaystyle 27$ square inches

$\displaystyle 28$ square inches

Correct answer:

$\displaystyle 27$ square inches

Explanation:

To find the perimeter of any object, simply add the length of each side together. The best answer is:

$\displaystyle 27$ square inches

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #4 : Perimeter Of A Triangle

Example Question #64 : Perimeter

Example Question #65 : Perimeter

Example Question #4 : Perimeter Of A Triangle

Example Question #1 : Perimeter Of A Triangle

Example Question #331 : Geometry

Example Question #12 : Perimeter Of A Triangle

Example Question #332 : Geometry

Example Question #333 : Geometry

Example Question #334 : Geometry

All Pre-Algebra Resources

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