Geometry Second Semester Review
1. Find the lateral area, total area and volume of the following figures.
a)
b)
c)
LA_______
TA_______
Vol_______
LA________
TA________
Vol________
LA_______
TA_______
Vol_______
2. A regular polygon has a perimeter of40 and apothem of 5. Find the area.
3. An equilateral triangle has sides 10 cm long. Find the area.
4. Find x if the area of
the trapezoid is 52.
5. Find the median and
the area of the trapezoid.
14
x
M
8
12
10
6
6. Find the area of the kite
with diagonals
9 and 14.
B
A
E
7. Find the area of a rhombus
whose perimeter is 20 and
whose diagonal is 8.
C
D
8. Find the area of a circle
whose diameter is 10.
9. Find the circumference of a circle
whose area is 49π .
10. Find the area of a sector with
radius 12 and a 45° arc.
11. The measure of the arc of segment
is 90°. The radius is 10. Find the
area of the segment.
A
O
B
12. Name the four Pythagorean triples_____________________________
13. Find x and y
a.
b.
c.
x
10
y
9
x
x
45
30
6
y
60
y
x_____ y_____
x_____ y_____
14. Find x
a.
x_____ y______
b.
c.
10
12
7
x
x
x________
x________
d.
x________
e.
x
x
9
x________
4
5
x________
15
15. Find the base of a triangle
with altitude 15 and area 60.
16. Find the area of a parallelogram
whose sides are 14 and 6 and whose
acute angle is 60°.
17. A circle of radius 6 is inscribed
in an equilateral triangle. Find
the area of the triangle.
18. Find the area of a regular hexagon
with sides 18 inches long.
B
d
e
19. State the following trigonometric ratios:
A
a) sin A________
b) cos A________
c) tan A________
20. Find x
a)
f
C
d) sin B__________
e) cos B__________
f) tan B__________
b)
x
100
x
18
70
37
x_______
21. Find A if
a) sin A = .6754
x________
b) cos A = .2315
c) tan A = 2.9761
22.
23.
K
B
5
6
8
D
M
6
R
10
3
A
P
O
Find: RP__________
OP__________
Find AD________
24. Does a triangle with sides
2, 5, 10 exist? Explain.
26. Find x
25. A scale model of the titanic is
is 18.5 inches long. The scale is
1:570. To the nearest foot, how long
was the titanic?
27. Find y.
28. Find z.
4
x
4
6
12
z
5
8
12
x_________
C
8
y
3
y_________
z__________
29. Given the prism as shown.
Find:
a) Lateral Area_________
b) Total Area__________
c) Volume____________
30) Given: FG = 2, GH = 8
HJ = 5,EM = 6
F
G
H
E
31) Find the area of a triangle with sides
3, 6, and 7.
O
M
Find: EO_________
EK_________
J
K
32) If two sides of a triangle are 6 and
10, state the restrictions on the
third side.
33) Complete: Describe how the following circles relate to one another:
_________________
_____________
34)
_____________
35)
The quadrilateral is ___________
about the circle.
The triangle is __________
in the circle.
36) Given the points A(-2, 3) and B(6,5)
a) Find the slope of the line joining them
b) Find the length of the segment joining them
c) Find the midpoint of the segment joining them
d) Find the slope of the line perpendicular and parallel to AB
37) a) If a radius is perpendicular to a chord, then it _______the chord
b) If a radius bisects a chord, then it is _____________to the chord.
38) If a2 + b2 = c2, the triangle is right. What must be true if:
a) a2 + b2 > c2
b) a2 + b2 < c2
39) If Donna Worry stands
4 feet tall and casts a 6 foot
shadow, and Bea Happy stands next
to her with an 8 foot shadow.
How tall is Bea?
40) Suppose the angle of elevation of
the sun is 40. If a flagpole casts a 40
foot shadow, how tall is the flagpole
(to the nearest foot)?
41) Simplify 5 147
42) Find the perimeter
A
AE = 2
BE = 3
Radius = 1
E
D
C
43)
44)
F
B
X
A
B
O
D
4
3
C
If the area of the smaller figure is 27, what is
the area of the larger figure?
45) State the restrictions on x.
40
x
70
Y
If AB < CD, then OX_____OY
46) What is the slope of a horizontal line?________________
47) What is the slope of a vertical line? _________________
48) Write the equation of a line with slope -2 and y-intercept 1.
49) Write the equation of a line through (-2,3) and (6,-4)
50) Find the slope of the line with equation 2x + 5y = 10
51) Write an equation for a circle with center (5, -3) and radius 3.
52) In ABC, B < A < C. State the sides in order from largest to smallest.