SAT Geometry

Mastering Geometry: SAT Geometry Quiz - part 1

The quiz consists of 200 questions, and the user will be presented with a unique set of 10 questions in each session for a diverse experience
Please note that answers cannot be deselected once chosen in the quiz, so make your choices carefully for an optimal testing experience.
Each question is meticulously crafted to mirror the complexity and diversity of geometric problem-solving you'll encounter in the SAT.
Use it as a targeted practice tool to identify and address specific areas of improvement.
Track your progress and see your geometric proficiency grow.

The diagram above shows a semicircular arch over a street that has a radius of 14 feet. A banner is attached to the arch at points A and B, such that AE = EB = 5 feet. How many feet above the ground are these points of attachment for the banner, correct to the nearest tenth of a foot?

13.1

16.1

15.1

14.1

None

In the figure above, x + y =

Write your answer in numbers only

In the figure above, what is the number of square units in the area of the shaded region?

12.5

11.5

13.5

14.5

None

In the figure above, the sum of the areas of the three shaded semicircles with centers at A, B, and C is X, and the area of the larger semicircle below the line is Y. If Y − X = kπ, what is the value of k?

None

In the figure above, OABC is a square and B is a point on the circle
with center O. If AB = 6, what is the area of the shaded region?

12(π − 2)

9(π − 1)

9(π − 2)

18(π − 2)

None

In the figure above, what is the ratio of RW to WS?

√2 to 1

3 to 1

√3 to 1

2 to 1

None

In the figure above, if the area of square ABCD is 64, what is the area
of equilateral triangle BEC?

8√3

16√3

12√3

None

In the figure above, what is the sum of the degree measures of the
marked angles?

180

120

It cannot be determined from the information given.

360

None

If each interior angle of a regular polygon measures 140°, how many
side does the polygon have

5 sides

6 sides

10 sides

9 sides

None

10.

In the figure above, what is y in terms of x?

3/2 x

4/3 x

3/4 x

None

11.

In the figure above, arc PBQ is one-quarter of a circle with center at O, and OABC is a rectangle. If AOC is an isosceles right triangle with AC = 8, what is the perimeter of the figure that encloses the shaded region? 16+ 4π

24-4√2 + 4π

24-4π

16-4√2 + 4π

16+ 4π

None

12.

How many different triangles are there for which the lengths of the
sides are 3, 8, and n, where n is an integer and 3 < n < 8?

Five

Four

Two

Three

None

13.

What is the area of a circle with a circumference of 10π?

√10π

100π

25π

5π

None

14.

Katie hikes 5 miles north, 7 miles east, and then 3 miles north again.
What number of miles, measured in a straight line, is Katie from her
starting point?

√113

√83

None

15.

In the figure above, what is the area of quadrilateral ABCD?

None

16.

If a bicycle wheel has traveled ƒ/π feet after n complete revolutions,
what is the length in feet of the diameter of the bicycle wheel?

ƒn/ π²

ƒ/nπ²

π²/ƒn

nƒ

None

17.

In the figure above, x =

4√3

4√2

None

18.

In the figure above, what is the value of x?
Write your answer in numbers only

19.

In the figure above, each arc is a semicircle. If S is the midpoint of PQ and Q is the midpoint of PR, what is the ratio of the area of semicircle PS to the area of semicircle PR?

1/9

1/8

1/12

1/16

None

20.

In the figure above, the vertices of square ACEG are the centers of four
quarter circles of equal area. What is the best approximation for the
area of the shaded region? (Use π = 3.14.)

0.86

0.64

1.57

0.79

None

21.

In the figure above, quadrilaterals ABED, BFGC, and ACHJ are
squares. If the area of equilateral ABC is 16 square inches, what is
the number of inches in the perimeter of polygon ADEBFGCHJA

None

22.

In the figure above, what is the area of parallelogram ABCD?

4√3

6√3

4√2

6√2

None

23.

In the figure above, ACDEFG is a regular hexagon. Sides DC and GA
are extended such that A is the midpoint of BG and C is the midpoint
of BD. If the area of △ABC is 9 square centimeters, what is the
number of centimeters in the perimeter of polygon ABCDEFG?

None

24.

In the figure above, OACB is a square with area 4x². If OA and OB are
radii of a sector of a circle O, what is the perimeter, in terms of x, of the
unbroken figure?

4(x + 2π)

x(4 + 3π)

x(3 + 4π)

x(6 + 4π)

None

25.

Brand X paint costs \$14 per gallon, and 1 gallon provides coverage of
an area of at most 150 square feet. What is the minimum cost of the
amount of brand X paint needed to cover the four walls of a rectangular
room that is 12 feet wide, 16 feet long, and 8 feet high?
Write your answer in numbers only

26.

The circle shown above has center O and a radius length of 12. If P is
the midpoint of OA and AB is tangent to circle O at B, what is the area
of the shaded region?

81π

128π

96π

120π

None

27.

Two hikers started at the same location. One traveled 2 miles east and
then 1 mile north. The other traveled 1 mile west and then 3 miles
south. At the end of their hikes, how many miles apart were the two
hikers?

None

28.

In the figure above, PA is tangent to circle O at point A, PB is tangent
to circle O at point B. Angle AOB measures 120° and OP = 24/π What is
the length of minor arc AB?

None

29.

If the coordinates of the endpoints of a diagonal of a square are (−2, −3) and (5, 4), what is the number of square units in the area of the square?

None

30.

If the equation of a circle is x²− 10x + y²+ 6y = −9, which of the
following lines contains a diameter of the circle?

y = 2x − 7

y = −2x + 13

y = 2x + 13

y = −2x + 7

None

Time's up

Mastering Geometry: SAT Geometry Quiz - part 1

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