SAT Math : Plane Geometry

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Rectangles

Two circles of a radius of  each sit inside a square with a side length of .  If the circles do not overlap, what is the area outside of the circles, but within the square?

Possible Answers:

Correct answer:

Explanation:

The area of a square = \dpi{100} \small side^{2}

The area of a circle is \dpi{100} \small \pi r^{2}

Area  = Area of Square \dpi{100} \small - 2(Area of Circle) =

Example Question #191 : Plane Geometry

The width of a rectangle is .  The length of the rectangle is .  What must be the area?

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is:

Substitute the variables into the formula.

Example Question #192 : Plane Geometry

Find the area of a rectangle with side length 7 and 9.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the area of a rectangle.

Substitute in the side length of 7 and width of 9.

Thus,

Example Question #193 : Plane Geometry

Find the area of a rectanlge given width is 2 and length is 3.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the area of a rectangle. Thus,

Example Question #194 : Plane Geometry

A parallelogram with right angles has side lengths of and . What is its area?

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

Remember that a parallelogram with right angles is a rectangle. With that in mind, all you need to do is multiply those side lengths together, knowing that they are the length and width of a rectangle:

Example Question #195 : Plane Geometry

Find the area of a rectangle given width 6 and length 9.

Possible Answers:

Correct answer:

Explanation:

To solve, simply multiply the width by the length. Using the formula, you get the answer as follows:

Additionally, you can alternatively solve this problem by drawing out a rectangle, creating 6 horizontal lines and 9 vertical ones, and then adding up the squares to reach your answer.

Example Question #196 : Plane Geometry

You have a poster of one of your favorite bands that you are planning on putting up in your dorm room. If the poster is 3 feet tall by 1.5 feet wide, what is the area of the poster?

Possible Answers:

Correct answer:

Explanation:

You have a poster of one of your favorite bands that you are planning on putting up in your dorm room. If the poster is 3 feet tall by 1.5 feet wide, what is the area of the poster?

Area of a rectangle is found via:

Example Question #332 : Plane Geometry

If the area Rectangle A is  larger than Rectangle B and the sides of Rectangle A are  and , what is the area of Rectangle B?

Possible Answers:

Correct answer:

Explanation:

Example Question #18 : Rectangles

Three of the vertices of a rectangle on the coordinate plane are located at the origin, , and . Give the area of the rectangle.

Possible Answers:

Correct answer:

Explanation:

The rectangle in question is below:

Rectangle 3

The lengths of the rectangle is 10, the distance from the origin to ; its width is 7, the distance from the origin to . The area of a rectangle is equal to the product of its length and its width, so multiply:

Example Question #197 : Plane Geometry

What is the length of the diagonal of a rectangle that is 3 feet long and 4 feet wide?

Possible Answers:

6\ feet

8\ feet

5\ feet

4\ feet

7\ feet

Correct answer:

5\ feet

Explanation:

The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 3 and 4. Using the Pythagorean Theorem:

3^{2}+4^{2} = hypotenuse^{2}

25 = hypotenuse^{2}

hypotenuse = 5

Therefore the diagonal of the rectangle is 5 feet.

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