The figure shows four smaller squares in the corners of a large square. the smaller squares have sides of length 1cm, 2cm, 3cm and 4cm in anticlockwise order and the sides of the large square have length of 11cm. What is the area of the shaded quadrilateral? (see attachment)

B. 36

Step-by-step explanation:

The shaded quadrilateral has a shape of a trapezium.

Area of a trapezium = (a + b)h

where: a is the side length parallel to the base, b is the base and h is the height.

The height of the figure = 11 - (4 + 1)

                                        = 11 - 5

                                        = 6

The height of the figure is 6 cm.

The length of its base = 11 - (1 + 2)

                                    = 11 - 3

                                    = 8

The length of its base is 8 cm.

The length of the side parallel to base = 11 - (4 + 3)

                                     = 11 - 7

                                     = 4

The parallel side length to base is 4 cm.

Area of quadrilateral = (a + b)h

                                     = (4 + 8)6

                                    = 12 x 3

                                    = 36

Area of quadrilateral = 36

step-by-step explanation:

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answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.