Geometry

In the figure above, two searchlights S1 and S2 are located 10,000 feet apart; each covers an area of radius 10,000 feet, and each is located 8,000 feet from the railroad track. To the nearest 1,000 feet, what is the total length x of track spanned by the searchlights?

Square RSTU shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for T to be in the position where S is now shown. The number of degrees through which RSTU is rotated is

In ΔPQS above, if PQ =3 and PS = 4, then PR =?

The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?

If each side of ΔACD above has length 3 and if AB has length 1, what is the area of region BCDE?

A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by n meteres, What is the area of the rug in square meters?

Each step of a staircase is 0.25 meter wide and 0.20 meter high, as shown in the figure above. All angles shown in the figure are right angles. If the height of the staircase is 3.6 meters and the landing at the top of the staircase is 1 meter wide, how long, in meters, is AB?

The volume of a box with a square base is 54 cubic centimeters. If the height of the box is twice the width of the base, what is the height, in centimeters?

In the figure above, what is the value of 2x - y?

In the figure above, two rectangles with the same dimensions overlap to form the shaded region. If each rectangle has perimeter 12 and the shaded region has perimeter 3, what is the perimeter of the resulting figure?

The figure above shows the shape of a sign to be placed in front of a flower store. The sign has a semicircle on each side of the square. If the sign is 3 centimeters thick and if each side of the square is 50 centimeters long, what is the volume, in cubic centimeters, of the sign?

In the figure above, the five circles have points in common as shown. P is the center of the largest circle, Q and R are centers of the medium-sized circles, and Q, P, and R are points on a straight line. What fraction of the largest circular region is shaded?

The number of diagonals of a polygon of n sides is given by the formula d=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?

If the area of the circle above is 64 π π , what is the value of k ?

If l1 || l2 in the figure above, what is the value of x?

In the figure above, square CDEF has area 4. What is the area of △ ABF?

An enclosed rectangular tank with dimensions 2 meters by 3 meters by 4 meters is filled with water to a depth of 1 meter as shown by the shaded region in the figure above. If the tank is turned so that it rests on one of its smallest faces, the depth, in meters, of the water will be

What is the value of x + y in the figure above? (1) w= 95 (2) z = 125

In the figure above, PQR and STU are identical equilateral triangles, and PQ = 6. What is the perimeter of polygon PQWTUVR? (1) Triangle SWV has perimeter 9. (2) VW has length 3.5.

In the parallelogram shown, what is the value of x? (1) y = 2x (2) x + z = 120