Perimeter, Area, Volume
An octagon has a side length of 2 inches. What is the octagon’s perimeter in inches?
16 inches.
If a point on a grid is at (5,2), and then the point reflects on the x-axis, then what is the position of the reflected point?
(5,-2).
An 8-foot-by-8-foot square connects with two triangles with 8-feet bases and heights of 12.5 feet. What is the total area of the shapes in square feet?
164 square feet.
A square has four points: A (-1,2), B (-3,2), C (-3,4), and D (-1,4). If the square translated 5 to the right, what are the four new points?
A (4,2), B (2,2), C (2,4), and D (4,4).
A 2.5-foot-by-2.5-foot-2.5-foot cube connects with a triangular prism with a 2.5-foot-by-2.5-foot base and a height of 3 feet. Presuming the top of the cube and the base of the triangular prism disappear, what is the total surface area of the shape in square feet?
55 square feet.
A circle’s center on a grid is at (-3,-8). If the circle rotated 270 Degrees with the origin as the point of rotation, what is the new center of the circle?
(-8,3).
A cylinder has a 7.5-inch diameter and a height of 12 inches. Within the cylinder are three 4-inch diameter spheres. What is the volume of the cylinder without the spheres in cubic inches (round to the nearest hundredth)?
1969.78 cubic inches (close numbers are fine).
A square has four points: A (3,5), B (8,5), C (8,10) and D (3,10). If the square rotated 180 Degrees with the origin as the point of rotation, and then dilated by 2 based upon the origin, what are the four new points?
A (-6,-10), B (-16,-10), C (-16,-20), and D (-6,-20).
A company makes a water bottle out of a cylinder with a 3.5-inch diameter and a height of 4 inches, while connecting the cylinder to a cone with a 3.5-inch diameter and a height of 2 inches. The company removes the top of the cone (the top representing a cone with a 1-inch diameter and a height of 0.57 of an inch), and places a cylinder with a 1-inch diameter and a height of 0.57 of an inch as a cap. Presuming that the top of the body cylinder, the bottom of the body cone, and the bottom of the cap cylinder disappear, how much plastic per square inch does a water bottle need for making (round to the nearest hundredth)?
69.63 square inches (close numbers are fine).
A triangle has three points: A (2,3), B (5,6), and C (4,9). If the triangle dilated to a scale factor of five based upon the origin, and then translated 2 up and 5 to the left, what are the three new points?
A (5,17), B (20,32), and C (15,47).