Find the area of the polygon

Mathematics

1 answer:

Helen [10]4 years ago

8 0

Answer:

Step-by-step explanation:

Assuming a perpendicular line(apotherm) is extended from the midpoint of the polygon to the midpoint of one of its sides, then we can determine the length of the apotherm by applying Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Let a represent the apotherm

Hypotenuse = 4

Apotherm = a

Opposite = a(apotherm = length of each side/2)

Therefore,

4² = a² + a²

16 = 2a²

a² = 16/2 = 8

a = √8 = 2√2

The formula for determining the area of a polygon is expressed as

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 6

Therefore,

Area = (2√2)² × 6 × tan(180/6)

Area = 48 × tan 30

Area = 27.2

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What is the approximate scale factor dilating from the red image to the blue image?Explain how you figured this out.

Lorico [155]

If the shape on the red image is scaled to the shape on the blue image, the scale factor is 0.2777.

Explanation:

The original shape's base in the red image is measured. The base of the red image is measured to be 9 units. Now we measure the same side of the blue image. The base of the blue image is measured to be 2.5 units. So after scaling, the length of the painting will be 2.5 units.

To calculate the scale factor, we divide the measurement after scaling by the same measurement before scaling. In this case, it is the base of both images. So The scale factor = $\frac{baselengthbeforescaling}{baselengthafterscaling}$ = $\frac{2.5}{9}$ = 0.2777.
So the red image is dilated by a scale factor of 0.2777 to produce the blue image.