If the diagonal is 10 we know all sides are equal so from pythagoraen theorem each side is 7.07 inch length
Area = 7.07 x 7.07 = 50
Using Pythagoras' theorem which says that the square on the hypotenuse (in this case the diagonal) is equal to the sum of the squares on the other two sides (which in the case of a square would be equal in length). so if the diagonal measured 10 units, the square on the diagonal would be 100 square units. And as this = 2*the squares on the other sides, the square on one side would be 100/2 = 50 square units. As a square has sides of equal length the square on one side is actually the area of the square. i.e. the area of a square with a diagonal of 10 units is 50 square units. or generically the area of a square with a diagonal of length 'x' = (x2)/2
The diagonal is 15.620 meters.
If the circle is inscribed in the square, the side length of the square is the same as the diameter of the circle which is twice its radius: → area_square = (2 × 5 in)² = 10² sq in = 100 sq in If the circle circumscribes the square, the diagonal of the square is the same as the diameter of the circle; Using Pythagoras the length of the side of the square can be calculated: → diagonal = 2 × 5 in = 10 in → side² + side² = diagonal² → 2 × side² = diagonal² → side² = diagonal² / 2 → side = diagonal / √2 → side = 10 in / √2 → area _square = (10 in / √2)² = 100 sq in / 2 = 50 sq in.
The radius of a square is the radius of the circumcircle, ie the distance from the centre of the square to any vertex, which is half the length of the diagonal of the square. Using Pythagoras: diagonal^2 = side^2 + side^2 → diagonal = √(2 x side^2) area = side^2 → diagonal = √(2 x area) radius = 1/2 x diagonal = 1/2 x √(2 x area) → radius = 1/2 x √(2 x 72 sq in) = 1/2 x √(144 sq in) = 1/2 x 12 in = 6 in.
Assuming you are talking about a rectangular area, the diagonal would be found using the Pythagorean Theorem. 5^2 + 10^2 = d^2, so 125 = d^2, then take square root of both sides. This means the diagonal is approximately 11.18 feet. It is exactly 5√5 feet.
The area of square is : 100.0
Using Pythagoras' theorem which says that the square on the hypotenuse (in this case the diagonal) is equal to the sum of the squares on the other two sides (which in the case of a square would be equal in length). so if the diagonal measured 10 units, the square on the diagonal would be 100 square units. And as this = 2*the squares on the other sides, the square on one side would be 100/2 = 50 square units. As a square has sides of equal length the square on one side is actually the area of the square. i.e. the area of a square with a diagonal of 10 units is 50 square units. or generically the area of a square with a diagonal of length 'x' = (x2)/2
The garden's diagonal is 10 meters.
Area = 50 cm2
If the area of a square is 100, then its side length is 10. If we draw in a diagonal, then we know by the Pythagorean formula that the diagonal's length is sqrt(10^2 + 10^2) = sqrt(200) = 10*sqrt(2).The square root of 2 is approximately 1.414, so the diagonal's length is approximately 10*1.414 =14.14* The diagonal of any square is the side length times (sq rt 2).
The diagonal is 15.620 meters.
If diagonal is 10 then each side is sqrt 50 (Pythagoras) and area is sqrt 50 x sqrt 50 ie 50
It is 10 metres.
If the circle is inscribed in the square, the side length of the square is the same as the diameter of the circle which is twice its radius: → area_square = (2 × 5 in)² = 10² sq in = 100 sq in If the circle circumscribes the square, the diagonal of the square is the same as the diameter of the circle; Using Pythagoras the length of the side of the square can be calculated: → diagonal = 2 × 5 in = 10 in → side² + side² = diagonal² → 2 × side² = diagonal² → side² = diagonal² / 2 → side = diagonal / √2 → side = 10 in / √2 → area _square = (10 in / √2)² = 100 sq in / 2 = 50 sq in.
14 The ratio of the side of a square to the diagonal is 1.4.
The radius of a square is the radius of the circumcircle, ie the distance from the centre of the square to any vertex, which is half the length of the diagonal of the square. Using Pythagoras: diagonal^2 = side^2 + side^2 → diagonal = √(2 x side^2) area = side^2 → diagonal = √(2 x area) radius = 1/2 x diagonal = 1/2 x √(2 x area) → radius = 1/2 x √(2 x 72 sq in) = 1/2 x √(144 sq in) = 1/2 x 12 in = 6 in.
Two adjacent sides of a square and the diagonal joining their ends froms a right angle triangle. The legs of the triangle are 10 ft each and the diagonal is the hypotenuse. By pythagoras, diagonal = sqrt(102 + 102) = 10*sqrt(2) = 14.142 ft (to 3 dp).