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There are a square and an isosceles right triangle in the figure above, and the whole area is 5/2. What is the value of x? Give your answer to the nearest 0.01.
A rectangular sidewalk is crowded with some spectators watching a parade. If the sidewalk is 10 feet wide and 1.5 miles long(1mile=5280 feet)and every spectator occupies 6 square feet, then how many spectators are there?
A man owns a square field, the area of the field is 16 square meters, now he wants the area to increase by 6 square meters and the field remains to be a square, then how many meters should the sides of the original field increase?
Give your answer to the nearest 0.1.

A parallelogram EHFG is inscribed in a rectangle ABCD，where point of E, H, F, G are all midpoint of respective sides of the rectangle. If the perimeter of the rectangle is 48 and the ratio of its length and width is 5 to 3，what is the area of the parallel EHFG？
Give your answer as a decimal.
The side length of a square is a, where 0 < a < 1

Quantity A

1

Quantity B

The area of a square with side length of 2a

The figure above represents the surface of a wall with an irregular shape, where all measurements are in meters and point P is $$10$$ meters from the bottom edge and $$10$$ meters from the left edge. The surface is to be painted, and one bucket of paint will cover $$170$$ square meters of the surface. If the bucket of paint will cover the part of the surface from the left edge to a vertical line that is $$x$$ meters from the left edge, which of the following is true?
The area of square S is twice the area of square T.

Quantity A

The length of a diagonal of square T

Quantity B

The length of a side of square S

AF//BE//CD，and AF=4，CD=4，BE=8，what is the area of polygon ABCDEF？

The top and bottom base of Trapezoid A (the left figure) are y and 2x, respectively, while the top and bottom base of Trapezoid B (the right figure) are x and 2y, respectively. Trapezoid A and B share the same height (y>x).

Quantity A

The area of trapezoid A

Quantity B

The area of trapezoid B

If a string AB and CD intersect at point P in a circle, then AP * BP = CP * DP. If AB = 20, and it is the diameter of a circle, CP = 12, DP = 3, what is the distance between the center point O and the point P?

AB is the diameter of the circle, point C is on the circle, BC=4, what is the area of the circle?


The figure represents a 5-foot-wide circular walkway that is bounded by two concentric circles. The outer boundary of the walkway is approximately how many feet longer than the inner boundary of the walkway?


A sphere, as shown above with a radius of 1 meter is rotating 360 degrees per second about its vertical axis. The speed, in meters per second, of a point on the sphere due to this rotation is in the range from
Dig a hole shaped as a square with a length of 1 foot on the ceiling and cover it with a hemisphere. How many inches `should the diameter of the hemisphere be so that the hemisphere covers the hole completely? (1foot=12 inches)

Triangle RST is inscribed in the circle with circumference of 20π and ∠R>90°

Quantity A

ST

Quantity B

10


The radii of the above two circles are both 3. If these two circles intersect at point P and point Q and each circle pass through the center of the other circle, then what is the total perimeter of the region (not counting the arc inside)?
Give your answer to the nearest tenths.

The area of the square inscribed in the circle is 196, what is the area of the shaded region? (π≈3.14) Give your answer to the nearest tenths.

In the figure above, a square is inscribed in a circle, if the area of shaded region is 5π, what is the area of the square?
A stone was dropped into a still pond and produced concentric circular ripples on the surface of the water. The radius of the outermost ripple increased at a constant rate of $$x$$ feet per second. If the area of the circular region enclosed by the outermost ripple was 400π square feet 10 seconds after the stone hit the water, what is the value of $$x$$?


The figure above shows five congruent circles each with radius 2 such that each of the five circles is tangent to two other congruent circles and to a smaller inner circle. The perimeter of the figure is composed of 5 line segments of length x and 5 circular arcs of length y. What is the perimeter of the figure?

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