SAT Geometry - Sriwiszy Education

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.

Every time the pedals go through a 360° rotation on a certain bicycle,
the tires rotate three times. If the tires are 24 inches in diameter, what
is the minimum number of complete rotations of the pedals needed for
the bicycle to travel at least 1 mile? [1 mile = 5,280 feet]

5280

281

561

None

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

16-4√2 + 4π

24-4√2 + 4π

16+ 4π

24-4π

None

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

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

3/2 x

4/3 x

3/4 x

None

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?

Two

Five

Four

Three

None

In the figure above, what is an equation of the line that contains
diagonal AC of square ABCD?

y = x − 1

y = 2x + 1

y = 1/2 x − 2

y = 2x − 8

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 pully system illustrated in the figure above, a belt with negligible
thickness is stretched tightly around two identical wheels represented
by circles A and B. If the radius of each wheel is 12/π inches and the
measure of ∠NPJ is 60°, what is the length of the belt?

$$48+\frac{32\sqrt{3}}{\pi}$$

$$80\pi \sqrt{3}$$

$$(32+48\sqrt{3})\pi $$

$$32+\frac{48\sqrt{3}}{\pi}$$

None

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

10.

The center of circle Q has coordinates (3, −2) in the xy-plane. If an endpoint of a radius of circle Q has coordinates R(7, 1), what is an equation of circle Q?

(x + 3)² + (y - 2)²= 25

(x − 3)² + (y + 2)²= 5

(x + 3)² + (y - 2)²= 5

(x − 3)² + (y + 2)²= 25

None

11.

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

None

12.

In the figure above, x + y =

Write your answer in numbers only

13.

In the figure above, P and Q are the midpoints of sides AB and BC,
respectively, of square ABCD. Line segment PB is extended by its own
length to point E, and line segment PQ is extended to point F so that
FE ⊥ PE. If the area of square ABCD is 9, what is the area of
quadrilateral QBEF?

21/8

23/8

27/8

22/7

None

14.

In rectangle ABCD, point P divides BC such that BP is 25% of the
length of BC. If the area of quadrilateral ABPD is 3/4, what is the area of
rectangle ABCD?

6/5

15/6

3/2

9/8

None

15.

If one pair of opposite sides of a square are increased in length by 20%
and the other pair of sides are increased in length by 50%, by what
percent is the area of the rectangle that results greater than the area of
the original square?

70%

77%

75%

80%

None

16.

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

9 sides

6 sides

10 sides

5 sides

None

17.

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?

9(π − 1)

12(π − 2)

18(π − 2)

9(π − 2)

None

18.

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.)

0.79

0.64

0.86

1.57

None

19.

In the figure above, the ratio of AD to DC is 3 to 2. If the area of △ABC
is 40, what is the area of △BDC?
Write your answer in numbers only

20.

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

21.

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

11.5

13.5

14.5

12.5

None

22.

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

4√2

6√2

4√3

6√3

None

23.

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

24.

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

25.

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 − 7

y = −2x + 13

y = 2x + 13

None

26.

In the figure above, x =

4√2

4√3

None

27.

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

1/16

1/12

None

28.

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(3 + 4π)

x(6 + 4π)

x(4 + 3π)

None

29.

In the figure above, OA⊥AB, and m∠BOC = 45°. If the coordinates of
point A are (0, 3) and the coordinates of point C are (7, 0), what is the
number of square units in the area of quadrilateral OABC?

None

30.

In rectangle ABCD above, arcs BP and CP are quarter circles with
centers at points A and D, respectively. If the area of each quarter circle
is π, what is the area of the shaded region?
4-π/2

8-2π

4-π/2

4-π

8-π

None

Time's up

Mastering Geometry: SAT Geometry Quiz - part 1

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