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How many pieces can we get at most if a square is split by three lines?
A triangle and a square have n intersection points, which of the following CANNOT be the value of n?

The side of square ABCD is 3. If each of the four sides is a hypotenuse of an isosceles right triangle, then what is the sum of the area of the four isosceles right triangles?

This figure shows a square with an area of 6 square inches.

* NOTE: One inch in the figure represents 3 foot.

Quantity A

The actual area the figure represents

Quantity B

50 square feet


A rectangular floor will be completely covered with square tiles, each of which has sides of length 6 inches. If tiles are laid side side with no space between them and no tiles are cut,then the number of tiles needed to cover the floor is 1,080. Which of the following could be the dimensions of the floor? (Note:12 inches=1 foot.)

In the figure shown above, the square ENFM is inscribed in the rectangle ABCD, point E and F are the midpoints of AB and CD. AB=16,GM=NH=3,what is the area of ENFM?

AEFD is a trapezoid, B is the midpoint of AE, ABCD is a square, and ∠CEF=90°

Quantity A

The area of square ABCD

Quantity B

The area of square CEF



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



As shown in the following figure, there is a vertical wall surface in the figure. The distance from point P to left edge is 10m, and the distance from point P to bottom edge is 10m. A barrel of pigment can be used to brush 170m^2 of the wall`s surface. If the barrel of pigment is used to brush the wall vertically from left edge, the total width of the surface that has been brushed to left edge is x m, what is the range of x?
There are two squares A and B,the area of A is twice as much as the area of B.

Quantity A

The length of a diagonal of square A

Quantity B

The length of a diagonal of square B



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 radius of two concentric circles differs by 5,by how much do the circumferences of the two circle differ?
There is a globe with a radius of 1 meter, now the globe will turn around one of its diameter in 360° per second. What is the range of the length one point on the globe will go in a second?

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