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Blizzard [7]
3 years ago
11

A trapezoid with area 55 square units is dilated by a scale factor of k. If k is equal to 2/3, find the area of the image.

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
5 0

Answer as a fraction = 220/9

Answer in decimal form = 24.44 approximately

=======================================================

Explanation:

The linear scale factor is k = 2/3.

The area scale factor is k^2 = (2/3)^2 = 4/9

We'll multiply the old area (55) by the area scale factor (4/9) to get the area of the smaller image.

55*(4/9) = 220/9 = 24.44 approximately

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Answer:

Formula for the Arc length is given by:

\text{Arc length} = 2 \pi r \cdot \frac{\theta}{360^{\circ}}

As per the statement:

radius of circle(r) = 6 units

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Use conversion:

1 rad = \frac{180}{\pi}

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then;

substitute these given values we have;

Use value of \pi = 3.14

\text{Arc length} = 2\cdot 3.14 \cdot (6) \cdot \frac{157.5^{\circ}}{360^{\circ}}

or

\text{Arc length} = 2\cdot 3.14 \cdot (6) \cdot 0.4375

Simplify:

\text{Arc length}=16.485

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