NAME ____________________
1.
Area Worksheet #1
An arc of a circle has length 18 cm and a radius of 12 cm.
The chord of the arc is pictured in the circle at right.
a.
What is the measure of the arc?
b.
What is the area of the sector
of the arc?
c.
What is the area of the larger
segment of the circle formed
by the arc and the chord.
12
2.
A triangle has sides of 8 cm and 15 cm
and an included angle of 60.
a.
What is the area of the triangle?
(radical form)
8
60
15
b.
3.
What is the length of the missing side?
A circle has a radius of 12 inches. A regular
octagon is inscribed in the circle. What is
the area of the region inside the circle but
outside the octagon?
4.
Two congruent circles each have areas
of 300 cm2. The circles overlap, so that
each of their centers is contained on the
other circle.
a.
What is the radius of each circle?
b.
How far apart are the centers of
the circles?
c.
What is the length of the
common chord AB?
d.
What is the area of the shaded
region bounded by both circles?
e.
What is the combined area of the
two unshaded regions?
A
P
O
B
A
P
f.
What is the total distance around
the outside perimeter of the two
circles?
O
B
NAME _____________________
5.
6.
The central angle of a sector is 135. The length of
the arc is 18.
a.
What is the radius of the circle?
b.
What is the area of the sector?
The vertex angle of an isosceles triangle is 120.
The longest side of the triangle is 30 cm.
a.
What is the length (in radical form) of the
congruent sides of the triangle?
b.
What is the area of the triangle?
c.
What is the radius of the circle that can be
circumscribed around the triangle?
d.
What is the area of the region between the
circle and the triangle?
7.
Find the combined areas of the regions R
and S in the diagram at right.
The smaller circle O has a radius of 6 cm
and the big circle P has a radius of 18 cm.
R
O
P
S
8.
What is the perimeter of the belt that can
be tightly placed around the two circles
(from question #10)?
9.
What is the area of the entire region
contained inside the belt?
10.
Find the area of the shaded region, in the
diagram at right. Diameter CD = 18 and
chord AB = 9.
What is the perimeter of the shaded region?
A
B
D
C
E
11.
In the diagram at right, sector EPD is a
quarter circle. AD=3, AP=12. Find the
combined areas of the regions R and S
that are inside the sector but not in
quadrilateral ABCP.
C
R
D
12.
S
B
The area of a sector of a circle is 10 in2 and
the length of the arc of that sector is 2.5 cm.
a. What is the radius of the sector?
b. What is the measure of the arc of the
sector?
c. To the nearest 100th, what is the area of the
smaller segment of the circle created by
the chord of the sector?
3
A
12
P
13.
An equilateral triangle and a square share a
common side, which is 6 2 cm long.
a.
What is the area of the shaded region?
b. What is the perimeter of the shaded
region?
c. What is the probability that a point
randomly selected inside the square is not
inside the triangle?
d. How far is the vertex of the triangle from
the side of the square?
14.
Circle P is inscribed in ABC, with mB=90. The
pieces of the hypotenuse intersected by the circle
are 5 cm and 12 cm.
A
a. What is the radius of the inscribed circle?
D
12
b. What is the area of the region between the circle and
the triangle?
P
B
c. What is the area of the circumscribed circle?
5
C
15.
The two tangent circles at right have radii of
12 cm and 36 cm. What is the area of the
shaded regions? What is the perimeter of the
shaded regions?
O
16.
An isosceles trapezoid is circumscribed
around a circle whose diameter is 183 cm.
The base angles of the trapezoid are each 60.
What is the area of the trapezoid? ________________
What is the length of the legs? ________________
17.
Find the area and perimeter of the shaded
region at left. The isosceles triangle has a
base of 14 and a perimeter of 64.
P
18.
In the diagram at right, ABC is given and
DE is parallel to the base BC. If the area of
trapezoid BCED is 72 cm2, find the area of
AED.
AD = 5 cm and BD = 2 cm
A
E
C
D
B