This topic involves applying the Pythagorean Theorem to find the area of squares, given the length of their diagonals. The focus is on calculating the area from the diagonal, requiring a conversion from the hypotenuse of a right triangle (formed by the square's diagonal) to the square's side length, and subsequently finding the area. Each problem presents a different diagonal length and requires computing the square's area, presented as real numbers to practice decimal calculations. The questions vary the diagonal lengths, enhancing skills in geometry and algebra through practical application of theoretical concepts.

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

more
View

Pythagoras in Squares - Diagonal Hypotenuse to Area Decimal Worksheet

Mobius Math Academy logo
Pythagoras in Squares - Diagonal Hypotenuse to Area Decimal
1
An svg image showing a math problem
Find the area of the square, given a diagonal of length 15
a
67.5
b
112.5
2
An svg image showing a math problem
Find the area of the square, given a diagonal of length 10
a
50
b
30
3
An svg image showing a math problem
Find the area of the square, given a diagonal of length 11
a
54.45
b
60.5
4
An svg image showing a math problem
Find the area of the square, given a diagonal of length 14
a
98
b
117.6
5
An svg image showing a math problem
Find the area of the square, given a diagonal of length 9
a
40.5
b
48.6
6
An svg image showing a math problem
Find the area of the square, given a diagonal of length 8
a
25.6
b
32
7
An svg image showing a math problem
Find the area of the square, given a diagonal of length 17
a
144.5
b
173.4
8
An svg image showing a math problem
Find the area of the square, given a diagonal of length 16
a
128
b
76.8