The Pythagorean Theorem

Parker rides his bicycle 5 miles south, then 5 miles west, then 7 more miles south. How far is he from where he started?

Express the distance between opposite corners of a cube of edge length 2 cm in simplest radical form.

An ant is crawling along the outside of the box below. What is the shortest distance he can walk from A to B along the path shown?

There is a shorter path from A to B in the diagram. What is the shortest distance along the outside of the box from A to B? Express your answer as a decimal rounded to the nearest tenth.

A 50-foot ladder rests against a wall so that the top of the ladder is 48 feet from the ground. As you start to climb the ladder it slips. If the top of the ladder drops 8 feet, how many feet does the bottom of the ladder slide from its original position?

Write an expression to represent the distance between opposite corners of a right rectangular prism whose edge lengths are a, b, and c.

A cylinder with a 4 cm diameter is 4 cm tall. What is the length of the shortest path from the base to a point at the top of the cylinder on the opposite side?

Riding your bicycle, you roll over a piece of gum which sticks to the bottom of your 24-inch diameter tire. You roll forward and the tire makes a 120 degree rotation. How high above the ground is the gum on the tire?

Equilateral triangle XYZ is inscribed in equilateral triangle ABC as shown. What is the ration of the area of triangle XYZ to the area of triangle ABC?

The vertices of a cube of side length 2 cm are connected to form a triangle as shown. What is the area of the triangle?

What is the height of a STOP sign (regular octagon) whose sides are one foot long?

Find the length AC in regular hexagon ABCDEF if the perimeter of the hexagon is 24 cm.

The midpoints of a hexagon are connected to form a smaller hexagon. What is the ratio of the perimeter of the small hexagon to the perimeter of the large hexagon?

What is the area of the smaller of the two concentric circles if the side length of the equilateral triangle is 8 cm?

An isosceles right triangle has hypotenuse length x. What is the area of the triangle in terms of x?

(-1, 4) and (2, -5)

(-7, -1) and (2, -10)

Square ABCD has side length 12 cm. What is the length of congruent segments BX, CX, and EX?

Congruent squares of side length 16 are inscribed in a circle as shown. Find the area of the circle in terms of pi.

Segment AB is trisected at its points of intersection with concentric circles of radius 7 cm and 9 cm. Find the length of segment AB.

The radius of the large semicircle is 2cm. What is the radius of the small semicircle?

Square ABCD has vertices A(1, -2) and C(4, 5). What is the area of the square?

Circle C passes through points X, Y, and Z on Congruent Squares. Find the area of each of the three squares if the radius of the circle is 15 cm.

A metal band is wrapped tightly around pipes of radius 3 cm and 9 cm. What is the length of the band? Express your answer in simplest radical form.

The top right corner of a standard 8.5 by 11 sheet of paper is folded down and left to align with the left edge, and the bottom right corner is folded up and left so that the fold lines look like the diagram below. What is the area of triangle ABC formed by the right edge and the fold lines?

Regular hexagon ABCDEF has sides measuring 6cm. What is the area of triangle ACE?