If the diagonal of a square is 10, find its area.

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{"content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1:","type":"text"},{"text":" The area ","type":"text"},{"type":"math_inline","attrs":{"latex":"A"}},{"text":" of a square with side length ","type":"text"},{"attrs":{"latex":"s"},"type":"math_inline"},{"text":" is ","type":"text"},{"attrs":{"latex":"A = s^2"},"type":"math_inline"},{"text":". The diagonal ","type":"text"},{"attrs":{"latex":"d"},"type":"math_inline"},{"type":"text","text":" of a square is related to the side length by:"}],"type":"paragraph"},{"attrs":{"latex":"d = s\sqrt{2} \implies s = \frac{d}{\sqrt{2}}"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2:","type":"text"},{"text":" Express the area in terms of the diagonal:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"A = s^2 = \left(\frac{d}{\sqrt{2}}\right)^2 = \frac{d^2}{2}"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" Substitute the given value ","type":"text"},{"type":"math_inline","attrs":{"latex":"d = 10"}},{"text":" into this formula:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"A = \frac{10^2}{2} = \frac{100}{2} = 50"},"type":"math_block"},{"content":[{"text":"So the area of the square is ","type":"text"},{"attrs":{"latex":"50"},"type":"math_inline"},{"text":".","type":"text"}],"type":"paragraph"}],"type":"doc"}

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