This math topic focuses on applying the Pythagorean theorem to solve problems related to finding the area of a square, given the length of a diagonal extending to the center of the square. This topic is designed to engage learners in processing square diagonal lengths into area calculations using decimal precision. Each problem provides two possible numerical answers, varying slightly, to prompt a deeper understanding of the underlying geometry and precision in calculations.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Pythagoras in Squares - Center Hypotenuse to Area Decimal Worksheet

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Pythagoras in Squares - Center Hypotenuse to Area Decimal
1
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Find the area of the square, given a diagonal to the center of length 11
a
145.2
b
242
2
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Find the area of the square, given a diagonal to the center of length 10
a
200
b
180
3
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Find the area of the square, given a diagonal to the center of length 8
a
115.2
b
128
4
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Find the area of the square, given a diagonal to the center of length 7
a
98
b
88.2
5
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Find the area of the square, given a diagonal to the center of length 13
a
338
b
405.6
6
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Find the area of the square, given a diagonal to the center of length 12
a
374.4
b
288
7
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Find the area of the square, given a diagonal to the center of length 15
a
450
b
405
8
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Find the area of the square, given a diagonal to the center of length 14
a
392
b
470.4