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Alex
2 years ago
6

3 semicircles are connected to 3 sides of a square. each side of the square measures 4 centimeters. what is the area of the comp

osite figure? (6π 4) cm2 (6π 16) cm2 (12π 4) cm2 (12π 16) cm2
Mathematics
1 answer:
puteri [66]2 years ago
5 0

The area of the composite figure  with 3 semicircles connected to 3 sides of a square is (6π+16)cm^{2}.

<h3 /><h3>What is a semicircle?</h3>

A semicircle is a plane shape that is a part of a circle divided into two equal parts through its diameter.

Analysis:

Since the semicircles are connected to 3 sides of a square 4cm, the diameter of the semicircle is 4cm.

Radius of semicircle = 4/2 = 2cm

Area of a semicircle = πr^{2}/2 = \pi(2)^{2}/2 = 2πcm^{2}

For three semicircles = 3 x 2πcm^{2} = 6πcm^{2}

Area of square = s^{2} = (4)^{2} = 16cm^{2}

Area of composite figure  = Area of 3 semicircles + area of square

Area of composite figure = (16 + 6π)cm^{2}

In conclusion, the area of the composite figure is  (16 + 6π)cm^{2}.

Learn more about  area of plane shapes: brainly.com/question/20475473

#SPJ4

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The equation of a hyperbola is  x^{2}/9 - y^{2}/4 = 1

What are the steps to Hyperbola equation ?

To find the equation of hyperbola, the following steps must be taken. You need to identify;

  • The coordinate of the center
  • The coordinate of the vertices
  • The coordinate of the foci

The general equation of a hyperbola can be expressed as

x^{2}/a^{2} - y^{2}/b^{2} = 1

From the graph, we have the following parameters

a = 3

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b = 2

b^{2} = 2^{2} = 4

The equation of a hyperbola can be expressed as

x^{2}/9 - y^{2}/4 = 1

The vertices = V(+/-a,0) = (+/-3,0)

The center = C(0,0)

The focus = F(+/-C, 0)

Where C^{2} = a^{2}  + b^{2}

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C = \sqrt{13}

Focus = F(+/- \sqrt{13}, 0)

The general equation for asymptote = +/- b/a X

= +/-2/3X

Therefore, the equation of a hyperbola can be expressed as

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