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3 years ago

If an interior angle of a regular polygon measures 140*, how many sides does it have?

Mathematics

1 answer:

Katen [24]3 years ago

5 0

Answer:

9 sides.

Step-by-step explanation:

N is the # of sides.

140 = ((n-2) x 180) / n

Multiply both sides by n

140 n = (n-2) x 180

Distribute the right side

140 n = 180 n - 360

Subtract 140 n and add 360 to both sides.

40 n = 360

n = 9

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2 years ago

Use the net to find the surface area of the prism 8in 15in 17in 9in

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Answer:

The surface area of the prism is 480 in².

Step-by-step explanation:

Given:

The prism dimensions are 8in 15in 17in and 9in.

Now, to find the surface area:

So, to get the surface area we put formula:

a=8in, b=15in, c=17in and h=9in.

Surface area = 2A+(a+b+c)h.

Whereas, $A=\sqrt{s(s-a)(s-b)(s-c)}$

And, $s=\frac{a+b+c}{2}$

Now, we find s first:

$s=\frac{a+b+c}{2}$

$s=\frac{8+15+17}{2}$

$s=\frac{40}{2}=20.$

Then, we get A :

$A=\sqrt{s(s-a)(s-b)(s-c)}$

$A=\sqrt{20(20-8)(20-15)(20-17)}$

$A=\sqrt{20(12)(5)(3)}$

On solving we get:

$A=\sqrt{3600}=60.$

Now, putting the value of A in the formula to get the surface area:

$Surface area = 2A+(a+b+c)h.$

$Surface area = 2\times 60+(8+15+17)9.$

$Surface area = 120+(40)9.$

$Surface area = 120+360.$

$Surface area = 480\ in^2.$

Therefore, the surface area of the prism is 480 in².

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3 years ago