Calculate Square Area from Diagonal
To find the area of a square given its diagonal, we can use a direct formula derived from the Pythagorean theorem.
Square Properties and Formula
Let 's' be the side length of the square and 'd' be the diagonal length. In a square, the diagonal divides it into two right-angled isosceles triangles. Applying the Pythagorean theorem (\(a^2 + b^2 = c^2\)):
- \(s^2 + s^2 = d^2\)
- \(2s^2 = d^2\)
The area of the square (A) is \(s^2\). Substituting A into the equation:
- \(2A = d^2\)
- \(A = \frac{d^2}{2}\)
Area Calculation
Given the diagonal \(d = 4\) cm:
- Substitute the value of the diagonal into the formula: \(A = \frac{(4 \text{ cm})^2}{2}\)
- Calculate the square of the diagonal: \(A = \frac{16 \text{ cm}^2}{2}\)
- Compute the final area: \(A = 8 \text{ cm}^2\)
Therefore, the area of the square is 8 cm\(^2\).
Similar Questions
What is the area of this parallelogram in sq.cm.? The measurements are in cms.
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- Calculate the length of the diagonal of a square if the area of the square is \(32\ cm^2\).
Important Questions from Plane Figures
- A rectangular grassy plot is 38 m long and 32 m wide. It has a gravel path of uniform width on the inside having an area of $600 \text{ m}^2$. The width of the path is:
- A river, 2 m deep and 45 m wide is flowing at the speed of 3 km per hour. The quantity of water that runs into the sea per minute is:
A regular hexagonal garden with each side measuring 14 metres is surrounded by a circular jogging track that has a radius of 21 metres from the centre of the hexagon. Find the sum of the perimeters of both shapes.
(Use $\pi = \frac{22}{7}$)- If a circle and a square have the same perimeter, then
What is the area of this parallelogram in sq.cm.? The measurements are in cms.
