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Sub 505 (Easy)|   Geometry|      
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Bunuel
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If a triangle of base 6 has the same area as a circle of radius 6, wha 19 Mar 2018, 00:00
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D
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Question Stats:

92% (00:48) correct 8% (01:02) wrong based on 83 sessions

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If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. \(6\pi\)

B. \(8\pi\)

C. \(10\pi\)

D. \(12\pi\)

E. \(14\pi\)
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D
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Bunuel
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If a triangle of base 6 has the same area as a circle of radius 6, wha 19 Mar 2018, 00:01
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Bunuel
If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. \(6\pi\)

B. \(8\pi\)

C. \(10\pi\)

D. \(12\pi\)

E. \(14\pi\)
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23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



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If a triangle of base 6 has the same area as a circle of radius 6, wha 19 Mar 2018, 00:11
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Bunuel
If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. \(6\pi\)

B. \(8\pi\)

C. \(10\pi\)

D. \(12\pi\)

E. \(14\pi\)
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Area of triangle = \(0.5*b*h\) (b is base and h is height)
Area of circle = \(\pi*R^2\) (r is radius)

base of triangle is 6 and radius of circle is 6.

\(0.5*6*h = \pi*6^2\)
\(h = 12\pi\)

Hence option D.

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If a triangle of base 6 has the same area as a circle of radius 6, wha 19 Mar 2018, 01:23
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Bunuel
If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. \(6\pi\)

B. \(8\pi\)

C. \(10\pi\)

D. \(12\pi\)

E. \(14\pi\)
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As the required calculation is straightforward, we'll just do it.
This is a Precise approach.

Writing what we're told as an equation, b*h/2 = pi*r^2.
That is, 6h/2 = 36pi so h = 12pi.

(D) is our answer.
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If a triangle of base 6 has the same area as a circle of radius 6, wha 19 Mar 2018, 13:47
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Area of triangle=1/2*base*Altitude= 1/2*6*Altitude =3*Altitude
Area of circle= π*r*r = π*6*6=36π

Given area of triangle= area of circle,
=>3*Altitude=36π
Altitude= 12π
Hence D is the answer
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If a triangle of base 6 has the same area as a circle of radius 6, wha 20 Mar 2018, 16:58
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Bunuel
If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. \(6\pi\)

B. \(8\pi\)

C. \(10\pi\)

D. \(12\pi\)

E. \(14\pi\)
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We can create the equation, in which h = height = altitude of the triangle. We equate the area of the triangle with base 6 to the area of the circle with radius 6:

6 x h x 1/2 = π x 6^2

3h = 36π

h = 12π

Answer: D
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If a triangle of base 6 has the same area as a circle of radius 6, wha 05 Jul 2022, 20:32
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If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle?

A. \(6\pi\)

B. \(8\pi\)

C. \(10\pi\)

D. \(12\pi\)

E. \(14\pi\)

It can be done like: 0.5*6*h = pi*6^2, that gives: h = 12pi
Answer: D
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