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3 years ago

Help me please with this geometry

Mathematics

1 answer:

Tasya [4]3 years ago

6 0

All Triangles are equilateral ( each side = 4)

Area of a Triangle is (B x H)/2. B being the base ( 4) & H the altitude.

WE know that altitude in an equilateral triangle, H = ( side x√3)/2

So H= (4√3)/2 = 2√3

The area of one triangle = (4 x 2√3)/2 = 4√3

And for the 3 triangles the lateral area = (4√3) x 3 = 12√3

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The horizontal distance between the center of circles P and Q is 11.70 units
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<h3>The horizontal distance between their centers?</h3>

From the figure, we have the centers to be:

P = (-5,4)

Q = (6,8)

The distance is then calculated using:

d = √(x2 - x1)^2 + (y2 - y1)^2

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d = √(6 + 5)^2 + (8 - 4)^2

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d = √137

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Hence, the horizontal distance between the center of circles P and Q is 11.70 units

<h3>The scale factor of dilation from circle P to Q</h3>

We have their radius to be:

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Q = 5

Divide the radius of Q by P to determine the scale factor (k)

k = Q/P

k = 5/2

k = 2.5

Hence, the scale factor of dilation from circle P to Q is 2.5