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The points of a six-pointed star consist of six identical equilateral
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02 Feb 2023, 04:28
02 Feb 2023, 04:28
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The points of a six-pointed star consist of six identical equilateral triangles, with each side 4 cm (see figure). What is the area of the entire star, including the center?
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\(48 \sqrt{3}\)
Re: The points of a six-pointed star consist of six identical equilateral
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18 Feb 2023, 02:50
18 Feb 2023, 02:50
Expert Reply
OE
Think of this star as a large equilateral triangle with sides 12 centimeters long, and three additional smaller equilateral triangles (shaded in the figure below) with sides 4 inches long. Using the same 30–60–90 logic you applied in problem 9, you can see that the height of the larger equilateral triangle is
\(6 \sqrt{3}\)
and the height of the smaller equilateral triangle is \(2 \sqrt{3}\)
The area of the large triangle is \(36 \sqrt{3}\)
The small ones are \(4 \sqrt{3}\)
The sum of both is \(48 \sqrt{3}\)
Think of this star as a large equilateral triangle with sides 12 centimeters long, and three additional smaller equilateral triangles (shaded in the figure below) with sides 4 inches long. Using the same 30–60–90 logic you applied in problem 9, you can see that the height of the larger equilateral triangle is
\(6 \sqrt{3}\)
and the height of the smaller equilateral triangle is \(2 \sqrt{3}\)
The area of the large triangle is \(36 \sqrt{3}\)
The small ones are \(4 \sqrt{3}\)
The sum of both is \(48 \sqrt{3}\)
gmatclubot
Re: The points of a six-pointed star consist of six identical equilateral [#permalink]
18 Feb 2023, 02:50
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