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SAT Practice Questions - Geometry
SAT Practice Questions - Geometry: 1,
2, 3, 4, 5,
6, 7,
8, 9,
10
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What is the area of the following square, if the length of BD is  ?
(A)
(B)
(C)
(D)
(E) |
1
2
3
4
5 |
Solution:
Step 1: We need to find the length of the side of the square in order to get the area.
Step 2: The diagonal BD makes two 45°-45°-90° triangles with the sides of
the square.
Step 3: Using the 45°-45°-90° special
triangle ratio  .
If the hypotenuse
is then the legs must be 2. So the length of the side of the square is 2.
Step 4: Area of square = s2 = 22 = 4
Answer: (D) 4
SAT Practice Questions - Geometry: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
In the figure below, what is the value of y ?
(A)
(B)
(C)
(D)
(E) |
40
50
60
100
120 |
Solution:
Step 1: Vertical angles being equal allows us to fill in two angles in the triangle that
y° belongs to.
Step 2: Sum of angles in a triangle = 180°.
So, y° + 40° + 80° = 180°
y° + 120° = 180°
y° = 60°
Answer: (C) 60
SAT Practice Questions - Geometry: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Two circles both of radii 6 have exactly one point in common. If A is a point on one circle and B is a point on the other circle, what is the maximum possible length for the line segment AB?
(A)
(B)
(C)
(D)
(E) |
12
15
18
20
24 |
Solution:
Step 1: Sketch the two circles touching at one point.
Step 2: The furthest that A and B can be would be at the two ends as shown in the
above diagram.
Step 3: If the radius is 6 then the diameter is 2 × 6 = 12 and the distance from A to
B would be 2 × 12 = 24
Answer: (E) 24
SAT Practice Questions - Geometry: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
A right circular cylinder has a radius of 3 and a height of 5. Which of the following dimensions of a rectangular solid will have a volume closest to the cylinder.
(A)
(B)
(C)
(D)
(E) |
4, 5, 5
4, 5, 6
5, 5, 5
5, 5, 6
5, 6, 6
|
Solution:
Step 1: Write down formula for volume of cylinder
V = πr2h
Step 2: Plug in the values
V = π × 32 × 5 = 45π
V = 45 × 3.142 = 141.39
Step 3: We now have to test the volume of each of the rectangular solids to find
out which is the closest to 141.39
(A) 4 × 5 × 5 = 100
(B) 4 × 5 × 6 = 120
(C) 5 × 5 × 5 = 125
(D) 5 × 5 × 6 = 150
(E) 5 × 6 × 6 = 180
Answer: (D) 5, 5, 6
SAT Practice Questions - Geometry: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Note: Figures not drawn to scale
In the figures above, x = 60. How much more is the perimeter of triangle ABC compared with the triangle DEF.
(A)
(B)
(C)
(D)
(E) |
0
2
4
6
8
|
Solution:
 
Note: Figures not drawn to scale
Step 1: Since x = 60°, triangle ABC is an equilateral triangle with sides all equal.
The sides are all equal to 8.
Perimeter of triangle ABC = 8 + 8 + 8 = 24.
Step 2: Triangle DEF has two angles equal, so it must be an isosceles triangle.
The two equal sides will be opposite the equal angles.
So, the length of DF = length of DE = 10.
Perimeter of triangle DEF = 10 + 10 + 4 = 24.
Step 3: Subtract the two perimeters.
24 – 24 = 0
Answer to Question 5: (A) 0
SAT Practice Questions - Geometry: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
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