Geometry

In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

A rectangular garden is to be twice as long as it is wide. If 360 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?

In the figure above, triangle ABC is equilateral, and point P is equidistant from vertices A, B, and C. If triangle ABC is rotated clockwise about point P, what is the minimum number of degrees the triangle must be rotated so that point B will be in the position where point A is now?

Circle.png [ 3.73 KiB | Viewed 74313 times ] The circle with center C shown above is tangent to both axes. If the distance from O to C is equal to k, what is the radius of the circle, in terms of k ?

Angles.png [ 9.95 KiB | Viewed 50676 times ] In the figure above, if z = 50, then x + y =

OPR.png [ 3.26 KiB | Viewed 38266 times ] In the rectangular coordinate system above, if point R (not shown) lies on the positive y-axis and the area of triangle ORP is 12, what is the y-coordinate of point R?

If O is the center of the circle above, what fraction of the circular region is shaded?

In the figure above, V represents an observation point at one end of a pool. From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the object?

The shaded portion of the rectangular lot shown above represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals

If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches?

In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

The figure above shows a circular flower bed, with its center at O, surrounded by a circular path that is 3 feet wide. What is the area of the path, in square feet?

A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

Door.png [ 6.35 KiB | Viewed 58175 times ] The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the figure above. If the trim is uniformly 1 foot wide, what fraction of the door's front surface is covered by the trim?

A certain rectangular window is twice as long as it is wide. If its perimeter is 10 feet, then its dimensions in feet are

Rectangular Floors X and Y have equal area. If Floor X is 12 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet?

The trapezoid shown in the figure above represents a cross section of the rudder of a ship. If the distance from A to B is 13 feet, what is the area of the cross section of the rudder in square feet?

In the figure above, if PQRS is a parallelogram, then y - x =

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?