The following figure shows an equllateral triangle Inscribed in a circle of radius 10 cm. Use the method of Example 6 in Section 6.2 to compute the area of the triangle. Give two forms for your answer: one with a square root and the other a calculator approximation rounded to two decimal places. cm? cm2
The following figure shows an equllateral triangle Inscribed in a circle of radius 10 cm. Use the method of Example 6 in Section 6.2 to compute the area of the triangle. Give two forms for your answer: one with a square root and the other a calculator approximation rounded to two decimal places. cm? cm2
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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The following figure shows an equilateral triangle inscribed in a circle of radius 10 cm. Give two forms for your answer: one with a square root and the other a calculator approximation rounded to two decimal places.
p.s Example 5 is included as a guide to solve the problem. thank you
Transcribed Image Text:The following figure shows an equilateral triangle inscribed in a circle of radius 10 cm. Use the method of Example 6 in Section 6.2 to compute the area of the triangle. Give two forms for your answer: one with a square root and the other a calculator approximation
rounded to two decimal places.
cm2 =
cm2
Transcribed Image Text:Figure 5
2 in.
2 in.
A
Solution
The idea here is first to find the area of triangle BOA by using the area formula from Example 4. Then,
since the pentagon is composed of five such identical triangles, the area of the pentagon will be five times
the area of triangle BOA. We will make use of the result from geometry that, in a regular n-sided polygon,
the central angle is 360° /n. In our case we therefore have
360°
ZBOA =
5
: 72°
We can now find the area of triangle BOA:
area = ab sin 0
= ;(2) (2) sin 72° = 2 sin 72° in.?
The area of the pentagon is five times this, or 10 sin 72° in.?. (Using a calculator, this is about 9.51 in.?.)
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