Download 7.2 Area of a Triangle Area of a triangle

Math 1330 Section 7.2
7.2 Area of a Triangle
Area of a Triangle
a
b
Recall the area of a triangle is given by A 
1
bh .
2
Area of a triangle a, b are the lengths of two sides of a triangle
is the angle between them.
Example 1: Find the exact area of the triangle.
A.
29
120
17
B.
M
53 O
.
4.1 m
36 O
J
5.6 m
A
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Math 1330 Section 7.2
Popper 15 question 1: Suppose you are looking at the top of a building from a spot on the sidewalk that is
exactly 500 feet away from the building. You notice that the angle of elevation to the top of the building is
12.3°. How tall is the building?
A. 109 feet
B. 107 feet
C. 489 feet
D. 2293 feet E. none of these
Example 2: Find the area of an isosceles triangle with legs measuring 7
inches and base angles measuring 22.5 ° .
Example 3: If the area of ABC is 20 square centimeters, a = 16 cm and c = 5 cm,
find all possible measures for angle B.
Example4: A regular hexagon is inscribed in a circle of radius 4m. Find the
area of the hexagon. Note: Regular means that all of the sides are equal and
all of the angles are equal
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Math 1330 Section 7.2
Popper 15 question 2: From the observation deck at the top of a downtown skyscraper, you can see your car in
a parking lot. You observe that the angle of depression to your car is 29.5°. The observation deck is 1450 feet
above the ground. How far is it from the building to your car?
A. 2945 feet
B.
2563 feet C. 1666 feet D. 820 feet E. none of these
Example 5: Find the area of a regular octagon with side length 16. (Hint: we
will use trigonometry and the geometric version of area of a triangle).
Area of a Segment of a Circle
You can also find the area of a segment of a circle. The shaded area of the
picture is an example of a segment of a circle.
O
B
A
To find the area of a segment, find the area of the sector with central angle θ
and radius OA. Then find the area of OAB . Then subtract the area of the
triangle from the area of the sector.
Example 6: Find the area of the segment of the circle with radius 8 and central angle measuring
. Give an
exact answer.
3
Math 1330 Section 7.2
Popper 15 question 3: An octagon is inscribed in a circle of radius 10. Find the area of the octagon.
A. 50√2
B. 25 √2
C. 200√2
D. 200√3
E. none of these
Example 7: In triangle ABC, the measure of Angle A is 2x, the length of AB is 5, and the length of AC is
sin
√
. If
, what is the area of the triangle.
Popper 15 question 4: The legs of an isosceles triangle are 16 cm each, and the measures of the base angles are
each 54 degrees. Find the area of the triangle.
A. 103.6 cm² B. 243.5 cm² C. 121.7 cm²
D. 207.2 cm²
E. none of these
4
Math 1330 Section 7.2
Popper 15 question 5: Find the exact area of the following triangle:
30
11
A.
B. 121√2
C.
√
D.
√
E. none of these
5