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In the figure above, triangle FGH is inscribed in the circle with center P. If the area of the circle is p, what is the area of triangle FGH ?
Correct answer is '0.96'. Can you explain this answer?
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In the figure above, triangle FGH is inscribed in the circle with cent...
When looking for the area of the triangle, remember that there are two basic methods: the direct method and the indirect method. With the direct method, we simply plug the base and height measurements into the formula A = bh/2, and with the indirect method, we find the area as the sum or difference of other areas. In this case, since we know the lengths of one of the sides, the direct method is probably best. But we will need to find the height as well.
Area of the circle is π: πr2 = π
Divide by π: r2 = 1
Take square root: r = 1
Now let’s mark up the diagram with this information. Since the radius of the circle is 1, the diameter FH has a length of 2. Now we can use the Pythagorean Theorem to find the length of GH, which is the height of the triangle if FG is taken as the base. (1.6)2 + (GH)2 = 22
Simplif y: 2.56 + (GH)2 = 4
Subtract 2.56: (GH)2 = 1.44
Take square root: GH = 1.2
(Notice that this is in fact a 3-4-5 triangle: if we multiply 3-4-5 by 0.4, we get 1.2-1.6-2.)
Plug into area formula:
Area of the circle is π: πr2 = π
Divide by π: r2 = 1
Take square root: r = 1
Now let’s mark up the diagram with this information. Since the radius of the circle is 1, the diameter FH has a length of 2. Now we can use the Pythagorean Theorem to find the length of GH, which is the height of the triangle if FG is taken as the base. (1.6)2 + (GH)2 = 22
Simplif y: 2.56 + (GH)2 = 4
Subtract 2.56: (GH)2 = 1.44
Take square root: GH = 1.2
(Notice that this is in fact a 3-4-5 triangle: if we multiply 3-4-5 by 0.4, we get 1.2-1.6-2.)
Plug into area formula:
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In the figure above, triangle FGH is inscribed in the circle with center P. If the area of the circle is p, what is the area of triangle FGH ?Correct answer is '0.96'. Can you explain this answer?
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In the figure above, triangle FGH is inscribed in the circle with center P. If the area of the circle is p, what is the area of triangle FGH ?Correct answer is '0.96'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about In the figure above, triangle FGH is inscribed in the circle with center P. If the area of the circle is p, what is the area of triangle FGH ?Correct answer is '0.96'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure above, triangle FGH is inscribed in the circle with center P. If the area of the circle is p, what is the area of triangle FGH ?Correct answer is '0.96'. Can you explain this answer?.
In the figure above, triangle FGH is inscribed in the circle with center P. If the area of the circle is p, what is the area of triangle FGH ?Correct answer is '0.96'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about In the figure above, triangle FGH is inscribed in the circle with center P. If the area of the circle is p, what is the area of triangle FGH ?Correct answer is '0.96'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure above, triangle FGH is inscribed in the circle with center P. If the area of the circle is p, what is the area of triangle FGH ?Correct answer is '0.96'. Can you explain this answer?.
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