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The area of the rectangle ABCD is and . Find the area of the shaded region.
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Important Questions on Geometry and Mensuration
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In a right-angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. The acute angles of the triangle are:
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If the sides of a triangle are in the ratio of , the perimeter is , then the length of the smallest side is:
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The number of distinct triangles with integral valued sides and perimeter as is:
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A polygon has diagonals. Then, what is the number of sides of the same polygon?
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PQRS is a square drawn inside square ABCD of side units by joining the midpoints of the sides AB, BC, CD, DA. The square TUVW is drawn inside PQRS, where T, U, V, W are the midpoints of SP, PQ, QR and RS. If the process is repeated an infinite number of times the sum of the areas of all the squares will be equal to:
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Suppose the same thing is done with an equilateral triangle of side , wherein the midpoints of the sides are connected to each other to form a second triangle and the midpoints of the sides of the second triangle are connected to form a third triangle and so on an infinite number of times—then the sum of the areas of all such equilateral triangles would be:
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If in the figure given below and OQ, PQ and OP are all joined by semicircles, then the perimeter of the figure (shaded area) is equal to:
