Question

Pentagon ABCDE is similar to pentagon PQRST. If the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, which
statement is true?
A.
The area of pentagon ABCDE IS 6 times the area of pentagon PQRST.
B.
The area of pentagon ABCDE is 12 times the area of pentagon PQRST.
C.
The area of pentagon ABCDE is 36 times the area of pentagon PQRST.
D.
The area of pentagon ABCDE IS 216 times the area of pentagon PQRST.​

Answer 1

Answer:

The answer is C

Step-by-step explanation:

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Answer 2

Any five-sided polygon or 5-gon is referred to as a pentagon. The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

What is a pentagon?

Any five-sided polygon or 5-gon is referred to as a pentagon. A basic pentagon's interior angles add up to 540°. A pentagon might be straightforward or self-intersecting.

We know the formula for the area of a pentagon, therefore, the area of the pentagon PQRST can be written as,

$A=\dfrac14\times \sqrt{5(5+25)}\times a^2$

Given that the side of the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, therefore, the area of the pentagon ABCDE can be written as,

$ABCDE=\dfrac14\times \sqrt{5(5+25)}\times (6a)^2\\\\ABCDE = \dfrac14\times \sqrt{5(5+25)}\times 36 \times a^2\\\\ABCDE = 36 \times A$

Hence, The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

Learn more about Pentagon:

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