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SAT Math : Quadrilaterals

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Example Questions

Example Question #21 : Quadrilaterals

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: 8*6 = 48

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Example Question #22 : Quadrilaterals

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:

A=w*l=6*9=54

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.

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Example Question #23 : Quadrilaterals

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:

12ft^2

4.5ft^2

4.5ft

6ft^2

Correct answer:

4.5ft^2

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:

A=l*w=3ft*1.5ft=4.5ft^2

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Example Question #24 : Quadrilaterals

If the area Rectangle A is $25\%$ larger than Rectangle B and the sides of Rectangle A are and , what is the area of Rectangle B?

Possible Answers:

Correct answer:

Explanation:

$A = \text{length}\: \times \:\text{width} = 10 \times 6 = 60$

A = 1.25 B

60 = 1.25B

$B =\frac{60}{1.25} = 48$

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Example Question #12 : How To Find The Area Of A Rectangle

Three of the vertices of a rectangle on the coordinate plane are located at the origin, (10, 0) , and (0, 7) . 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 (10,0) ; its width is 7, the distance from the origin to (0, 7) . The area of a rectangle is equal to the product of its length and its width, so multiply:

$A = 10 \times 7 = 70$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

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

Possible Answers:

$4\ feet$

$7\ feet$

$6\ feet$

$8\ feet$

$5\ feet$

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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Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

The length and width of a rectangle are in the ratio of 3:4. If the rectangle has an area of 108 square centimeters, what is the length of the diagonal?

Possible Answers:

15 centimeters

24 centimeters

18 centimeters

12 centimeters

9 centimeters

Correct answer:

15 centimeters

Explanation:

The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3x and 4x.

We also know the area, so we write an equation and solve for x:

(3x)(4x) = 12x²= 108.

x² = 9

x = 3

Now we can recalculate the length and the width:

length = 3x = 3(3) = 9 centimeters

width = 4x = 4(3) = 12 centimeters

Using the Pythagorean Theorem we can find the diagonal, c:

length² + width² = c²

9² + 12²= c²

81 + 144 = c²

225 = c²

c = 15 centimeters

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Example Question #201 : Sat Mathematics

Find the length of the diagonal of a rectangle whose sides are 8 and 15.

Possible Answers:

$\sqrt{17}$

$\sqrt{23}$

Correct answer:

Explanation:

To solve. simply use the Pythagorean Theorem where a=8 and b=15 .

Thus,

$c=\sqrt{a^2+b^2}=\sqrt{8^2+15^2}=\sqrt{289}=17$

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Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

Prism

The above figure depicts a cube, each edge of which has length 18. Give the length of the shortest path from Point A to Point B that lies completely along the surface of the cube.

Possible Answers:

$18 \sqrt{2}$

$18\sqrt{5}$

$18\sqrt{6}$

$18\sqrt{3}$

Correct answer:

$18\sqrt{5}$

Explanation:

The shortest path is along two of the surfaces of the prism. There are three possible choices - top and front, right and front, and rear and bottom - but as it turns out, since all faces are (congruent) squares, all three paths have the same length. One such path is shown below, with the relevant faces folded out:

Prism 2

The length of the path can be seen to be equal to that of the diagonal of a rectangle with length and width 18 and 36, so its length can be found by applying the Pythagorean Theorem. Substituting 18 and 36 for and :

$c = \sqrt{a^{2}+b^{2}}$

$= \sqrt{18^{2}+36^{2}}$

$= \sqrt{324+1,296}$

$= \sqrt{1,620 }$

Applying the Product of Radicals Rule:

$c = \sqrt{1,620 } = \sqrt{324} \cdot \sqrt{5 } = 18 \sqrt{5 }$ .

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Example Question #1 : How To Find The Length Of The Side Of A Rectangle

The two rectangles shown below are similar. What is the length of EF?

Sat_mah_166_02

Possible Answers:

Correct answer:

Explanation:

When two polygons are similar, the lengths of their corresponding sides are proportional to each other. In this diagram, AC and EG are corresponding sides and AB and EF are corresponding sides.

To solve this question, you can therefore write a proportion:

AC/EG = AB/EF ≥ 3/6 = 5/EF

From this proportion, we know that side EF is equal to 10.

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SAT Math : Quadrilaterals

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #21 : Quadrilaterals

Example Question #22 : Quadrilaterals

Example Question #23 : Quadrilaterals

Example Question #24 : Quadrilaterals

Example Question #12 : How To Find The Area Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #201 : Sat Mathematics

Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Side Of A Rectangle

All SAT Math Resources

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