Q&A for How to Find the Area of a Square Using the Length of its Diagonal

This shape is not a square, since it does not have equal sides. It is an irregular quadrilateral, either a trapezoid or an irregular shape with no name. Draw a right triangle inside the shape with the diagonal as the hypotenuse. If you have enough information to calculate the height and base of this right triangle (usually with trigonometry), you can use Pythagoras' Theorem to find the diagonal. The two diagonals will be different lengths, since the shape is not symmetrical.

Assuming it is a square or rectangle, you have to know the other dimension, too.

Suppose that the diagonal is 8. Square 8, so you will get 64. Now divide 64 by 2, you will get 32. Get the square root of 32. That is the length of the side of a square. The square root of 32 is equal to 4 square root of 2.

This problem is trying to get you used to working with algebraic terms. Although it looks strange at first, you can substitute (2x + 5) for the side length in any formula. In this case, start with the formula A = s x s. Substitute (2x + 5) for each s, then simplify as much as you can.

A square always has equal lengths. If your shape has four right angles, it is a rectangle. You can use Pythagoras' theorem to find the diagonal from the length and width of the rectangle: d^2 = l^2 + w^2.

The length is 12 ft if one of the sides is 12 ft. The length of the diagonal can be found using the Pythagorean Theorem (a^2+b^2=c^2). In this formula, a and b are the sides of the right triangle, and c is the long side or the hypotenuse. The diagonal (c) would be found with the equation 12^2+12^2=c^2. 144+144=c^2, 288=c^2, c=sqrt(288)=approximately 16.97. Therefore, the diagonal of a square that is 12 feet would be around 17 feet.

If the circle's diameter fits perfectly across the square, it must be equal to the side's square length. Divide this by two to get the circle's radius, then use the standard area formula for circles: Area = pi * r^2.

Start with the area formula A = s^2 and solve for s. (Hint: a square root will cancel out the exponent.)

Area = length X width 10.5 X 10.5 = 110.25 sq ft.

A square is a 2D shape, so therefore does not have a surface area. It only has an area, which is calculated by multiplying two sides together, or squaring one. as a square has equal edges.

Let s be one side and d be the diagonal. Find s. By the Pythagorean theorem, s² + s² = d² = 8² = 64. So 2s² = 64, and s² = 32. Then s = √32 = 5.66 units.

The area increases by 21%.

Multiply pi by the square of the radius.

The ratio of the triangle's area to the square's area is √3 / 4 : 1 (or 0.433 : 1).

The area is (2x - 8)² = 4x² - 32x + 64.

By the Pythagorean theorem we find that each side of the square measures 1.06 cm, so the perimeter is four times that, 4.24 cm. The side length is found this way: the Pythagorean theorem says that with sides a and b and diagonal c, a² + b² = c². In this case, a = b, and c = 1.5. So a² + b² = 2a² = 2.25, and a² = 1.125. Then a = 1.06.

The length of one side is the square root of 1024, which is 32.

They are the same thing. The area of a square whose side length is 2 is 4. 2 squared is also 4.

The perimeter is the length all the way around the square, consisting of four times the length of one edge.

It could be difficult to get a really accurate calculation of the area if you start with a diagonal. (It would be easier if you start with a side.)

It depends on your definition of "trapezium." In some parts of the world it means a quadrilateral with exactly two parallel sides (a "trapezoid" in other parts of the world). Elsewhere it means an irregular quadrilateral with no parallel sides. In the first instance the area formula is [(a + b) / 2](h), where a and b are the lengths of the two parallel sides, and h is the height. In the second case there is no formula. You have to divide the figure into subsections whose areas you can compute (squares, rectangles and triangles). Then add the areas together to get the total area.