Geometry

The figure above shows a path around a triangular piece of land. Mary walked the distance of 8 miles from P to Q and then walked the distance of 6 miles from Q to R. If Ted walked directly from P to R, by what percent did the distance that Mary walked exceed the distance that Ted walked?

A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?

If the length of a diagonal of a square is 2 √ x 2 x √ , what is the area of the square in terms of x ?

The figure above represents a semicircular archway over a flat street. The semicircle has a center at O and a radius of 6 feet. What is the height h, in feet, of the archway 2 feet from its center?

In the figure above, what are the coordinates of point R ?

The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length l and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?

The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?

In the figure above, what is the ratio of the measure of angle B to the measure of angle A?

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A flat patio was built alongside a house as shown in the figure above. If all angles shown are right angles, what is the area of the patio in square feet?

2018.OG.05.026.q.png [ 32.11 KiB | Viewed 51824 times ] In the figure shown, AC = 2 and BD = DC = 1. What is the measure of angle ABD?

If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

A closed cylindrical tank contains 36 π cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

When the figure above is cut along the solid lines, folded along the dashed lines, and taped along the solid lines, the result is a model of a geometric solid. This geometric solid consists of 2 pyramids each with a square base that they share. What is the sum of number of edges and number of faces of this geometric solid?

If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 7, and k?

In the figure shown, what is the value of v+x+y+z+w?

A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

A rectangular floor that measures 8 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters. If the carpet squares cost $12 apiece, what is the total cost for the number of carpet squares needed to cover the floor?