\(2^2+4^2+...+100^2-\left(1^2+3^2+...+99^2\right)\)
\(=\left(2^2-1^2\right)+\left(4^2-3^2\right)+...\left(100^2-99^2\right)\)
\(=\left(2-1\right)\left(2+1\right)+\left(4-3\right)\left(4+3\right)+...+\left(100-99\right)\left(100+99\right)\)
\(=1+2+3+...+100\)
\(=\frac{100.\left(100+1\right)}{2}=5050\left(cm^2\right)\)
Given that ABCD is a rectangle with AB = 12 cm, AD = 6 cm. M and N are respectively midpoint of segments BC and CD. Find the area of triangle AMN in square centimeters.
Let ABCD be the square with the side length 56cm. If E and F lie on CD, C respectively such that CF = 14cm and EAF = 45o then CE = ........cm.
Let ABCD be a trapezoid with bases AB, CD and O be the intersection of AC and BD. If the areas of triangle OAB, triangle OCD are 16cm2, 40cm2respectively and M is the midpoint of BD, then the area of the triangle AMD is .........cm2.
A square and a triangle have equal perimeters. The lengths of three sides of the triangle are 6.2cm, 8.3cm and 9.5cm. The area of the square is...
Given a rectangular box ABCD.A'B'C'D'. Its base is a rectangular with BD = 5 cm; AB = 3 cm. If BC' = \(\sqrt{41}\) cm, the lateral area of this rectangular box is ..... cm2
A trapezuim ABCD has two parallel sides AB and CD. The diagonals AC and BD intersect at E. If the areas of triangle CDE and CDB are 1 and 4 respectively, what is the area of the trapezuim ABCD
What is the maximum possible area, in , of a rectangle with a perimeter of 20cm?
A rectangle has a length of 60cm and a width of 30cm. It is cut into 2 indentical squares, 2 identical rectangles and a shaded small square. Find the area of the shaded square.
Find the area of the shaded square.
