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TRANSCRIPT
Quadrilaterals
Example 1. A city block is in the form of a parallelogram whose shorter
diagonal AB is perpendicular to side BC, as shown in the figure. The
shorter sides represent streets and the longer sides represent avenues. If
the distance between the avenues is 400ft and the length of each street is
500 ft, find the area of the block.
Quadrilaterals
2 2500 400DC
400
500 300
2000
3
AB
AB
2000
500 333333.33 . 37037.04 . .3
BC AB sq ft or sq yd
Quadrilaterals
Example 2. Find the area of the rectilinear figure shown, if it is the
difference between two isosceles trapezoids whose corresponding sides
are parallel.
Quadrilaterals
3
8 6
3 62.25
8
z
z
1 1
12 18 8 18 2 2.25 2.136 18 2 2.136 6 51.1322 2
A sqin
2 23 8 73y
8 2
73
2 732.136
8
x
x
Circle
Example 1. The section of a certain solid is bounded by two concentric
circles whose radii are 6.1 ft and 4.1 ft. Find the area of this section.
2
1
2
2
2 2 2 2
1 2
6.1
4.1
6.1 4.1 6.1 4.1
6.1 4.1 6.1 4.1 10.2 2 64.089
A
A
A A
sq ft
Circles
Example 2. A triangle is inscribed in a circle of radius 6 inches as
shown in the diagram. What is the area of the shaded polygon?
1 1
5 12 302 2
A bh in
If a triangle is inscribed in a circle with the
diameter as one side, it will always be a
right triangle.
Circles
Example 4. Find the perimeter and area enclosed by the track ABCDEF in the
figure?
2 440 2 2 70 440 2 1319.82Total Perimeter r ft
22 70 440 70 2 76993.804Total Area r bh sq ft
Circles
Example 5. Each of the four circles shown in the figure is tangent to the other
three. If the radius of each smaller circle is a = 2.71, find the area of the
largest circles.
Circles
2.71sin60
3.13
3.13 2.71 3.31 5.84
x
x
radius a
22 5.84 107.14A r squnit
Circles
Example 6. The plane area shown consists of an isosceles trapezoid (non-
parallel sides equal) and a segment of a circle. If non-parallel sides are
tangent to the segment at points A and B, find the area of the composite
figure.
Circles
3 2cos60
3"
R
R
sin603
2.598"
3 2.598 0.40"
h h
R
h
R h
221 1 1 1
3 60 3 2.5982 2 2 180 2
4.712 3.897 0.815"
segment of acircle
segment of acircle
A R ab
A
Circles
4.6tan30
7.967"
x
x
1 1
3 18.934 4.6 50.452 2
trapezoidA a b h
3 2 3 2 7.967 18.934"x
0.815 50.45 51.265"totalA