Question

area of a pentagon with numbers 4, 6, 16, 9, answer choices: A:107^2 B: 116^2 C:150^2 D:182^2

Answer 1

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Answer 2

To find the area of a pentagon, you can use the formula: 1/4 * √(5(5+2√5) * (a^2 + c^2 - 2ac * cos(72))).

Given the side lengths of the pentagon are 4, 6, 16, 9, the formula becomes:

1/4 * √(5(5+2√5) * ((4^2 + 6^2 - 2 * 4 * 6 * cos(72)) + 16^2 - 9^2 - 2 * 16 * 9 * cos(72)))

Calculate the cosine of 72 degrees: cos(72) ≈ 0.309

Plugging these values into the formula:

1/4 * √(5(5+2√5) * ((16 + 36 - 48 * 0.309) + 256 - 81 - 288 * 0.309))
1/4 * √(5(5+2√5) * (4.37 + 256 - 81 - 88.752))

1/4 * √(5(5+2√5) * (178.618))

1/4 * √(5(5+2√5) * 178.618)

1/4 * √(5 * (5+2√5) * 178.618)

1/4 * √(5(5+2√5) * 178.618)

1/4 * √(5(5+2√5) * 178.618)

1/4 * √(5 * (5+2√5) * 178.618)

1/4 * √(893.09 * 5+ 2√5)

1/4 * √(4465.45 + 1786.18√5)

1/4 * √(4465.45) + √(1786.18)√5)

1/4 * √(66.88) + 42.301√5

1/4 * 8.18 + 42.301√5

1/4 * 8.18 + 42.30 = 8.295 + 210.753 = 219.048

Therefore, the area of the pentagon is approximately 219.048 square units, which when squared equals 219.048^2.

The closest answer choice to this result is option B: 116^2.

Answer 3

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