SAT Math - Perimeter | Practice Hub

If the sides of a triangle are , , and , what is the perimeter?

$\frac{1}{2}x+\frac{7}{2}$

$\frac{13}{2}x+7$

Explanation

The perimeter of a triangle is the sum of all three sides of the triangle.

Add all the side lengths.

Expand the terms in the bracket and remove all parentheses.

Combine like-terms.

The answer is:

What is the perimeter of a right triangle with a base of 6, and a height of 8?

$\textup{Cannot be determined.}$

Explanation

Use the Pythagorean Theorem to determine the hypotenuse.

Substitute the base and height.

Square root both sides to find the hypotenuse.

Add the sides to determine the perimeter.

The answer is:

If the side length of a rectangle is 6 inches, what is the perimeter?

$\textup{Cannot be determined.}$

Explanation

A square can be a rectangle, but a rectangle cannot be a square. We cannot assume that the width is known given just the length of the rectangle. There is not enough information to determine the perimeter just by the side length alone.

The answer is: $\textup{Cannot be determined.}$

Thingy

Refer to the above figure. Quadrilateral is a square. What is the perimeter of Polygon ?

Explanation

$\overline{BE }$ is both one side of Square and the hypotenuse of $\Delta ABE$ ; its hypotenuse can be calculated from the lengths of the legs using the Pythagorean Theorem:

$BE = \sqrt{5^{2}+12^{2}} = \sqrt{25 + 144} = \sqrt{169} = 13$ .

Since Square has four congruent sides, each side has length 13.

The perimeter of Polygon is

Garden

Note: Figure NOT drawn to scale

Refer to the above figure, which shows a rectangular garden (in green) surrounded by a dirt path (in orange) seven feet wide throughout. What is the perimeter of the garden?

$264\textrm{ ft}$

$292\textrm{ ft}$

$132 \textrm{ ft}$

$146 \textrm{ ft}$

$306 \textrm{ ft}$

Explanation

The inner rectangle, which represents the garden, has length and width $(100 - 2\times 7) = 86$ feet and $(60 - 2\times 7) = 46$ feet, respectively, so its perimeter is

feet.

What is the perimeter of a rectangle if the area is 60, and one of the side length is 15?

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

Explanation

Write the formula for the area of the rectangle. We will need the length of the other side of the rectangle.

Let the known side length be the base.

Divide by 15 on both sides to get the height.

$\frac{60}{15}=\frac{15h}{15}$

There are two bases and two heights in a rectangle.

The perimeter is:

The answer is:

Find the circumference of a circle with diameter of 15.

$15\pi$

$30\pi$

$56.25\pi$

$49\pi$

$35\pi$

Explanation

The circumference of a circle is denoted by the formula $C=2*\pi*r$ where r is the radius of the circle. The problem gives us the diameter of the circle which must be used to find the radius.

$radius=\frac{Diameter}{2}=\frac{15}{2}=7.5$

Plug the radius into the formula for the area of a circle

$C=2*\pi*7.5=15\pi$

Hexagon 2

The image represents a track is a regular hexagon with perimeter one half of a mile.

Selena starts at Point A and runs clockwise to Point D. She then runs directly from Point D to Point A. How far does she run?

$2,200 \textup{ feet}$

$2,640 \textup{ feet}$

$1,760 \textup{ feet}$

$2,420 \textup{ feet}$

$3,080 \textup{ feet}$

Explanation

The perimeter of the hexagonal track is one half of a mile. One mile is equal to 5,280 feet, so one half of a mile is equal to

$\frac{1}{2} \times 5,280 = 2,640\textup{ feet}$

Each of the six congruent sides measures one sixth of this, or

$\frac{1}{6} \times 2,640 = 440\textup{ feet}$

The hexagonal track is recreated below, with its six radii constructed - the center is called .

Hexagon 3

The radii divide the hexagon into six equilateral triangles, so each of the radii has length equal to one side of the hexagon. Selena's path takes her along $\overline{AB}$ , $\overline{BC}$ , $\overline{CD}$ , $\overline{DO}$ , and $\overline{OA}$ - a path equivalent in distance to five sides of the hexagon. Therefore, Selena runs a distance of

$5 \times 440 = 2,200 \textup{ feet}$

If a side of a square has a length of , what is the perimeter?

Explanation

Step 1: Define Perimeter...

The perimeter of any shape is the sum of all the sides of that figure..

Step 2: Find how many sides a square has...

A square has sides.

Step 3: Calculate the perimeter...

Triangle

Note: Figure NOT drawn to scale.

Refer to the figure above, which shows a square inscribed inside a large triangle. What is the difference between the perimeter of the white trapezoid and the blue triangle?

$-10 +10 \sqrt{5}$

$-10 +10 \sqrt{2}$

$-10 +10 \sqrt{3}$

Explanation

One side of the white trapezoid is the hypotenuse of the small top triangle, which has legs 10 and 20. Therefore, the length of this side can be determined using the Pythagorean Theorem:

$c = \sqrt{10^{2}+ 20^{2}} = \sqrt{100 + 400} = \sqrt{500} = \sqrt{100} \cdot \sqrt{5} = 10 \sqrt{5}$

The trapezoid has perimeter

$30 + 20 + 20 + 10 \sqrt{5} = 70 + 10 \sqrt{5}$ .

The small top triangle has legs 10 and 20 and hypotenuse $10 \sqrt{5}$ , and, therefore, perimeter

$10 + 20 + 10 \sqrt{5} = 30 + 10 \sqrt{5}$ . The blue triangle, which is similar as a result of the parallelism of the opposite sides of the square, has short leg 20. Since the perimeter of two similar triangles is directly proportional to a side, we can set up and solve the proportion statement to find the perimeter of the blue triangle: