Title: M3.2 Perimeter, Circumference and Area
Course: Technical Math for Industry > Section: Module 3.2 Perimeter, Circumference and Area

Q: Troy is building a ramp for his toy cars. The plank he is using for the ramp is 8 feet long and is placed on a 2-foot-high box.

How far from the box is the bottom edge of Troy's ramp?
- 60 (Incorrect. You may have correctly used the Pythagorean Theorem to get , but you did not completely finish solving for b.)
- 6 (Incorrect. It appears that you just subtracted the 2 from the 8. The ramp is the hypotenuse of a right triangle. You need to use the Pythagorean Theorem:)
A: (a choice with no text)
Feedback: Incorrect. It appears that you used the Pythagorean Theorem with 2 and 8 as the legs. However, the ramp is the hypotenuse of the right triangle. The correct equation to use is:
Feedback: Correct. The ramp is the hypotenuse of a right triangle. Use the Pythagorean Theorem:

Q: Quadrilateral RSTQ is a parallelogram.

Which of the following relationships must be true?
A: (a choice with no text)
Feedback: Incorrect. Opposite sides and opposite angles in a parallelogram are congruent. Because and are adjacent sides in parallelogram RSTQ, they are not necessarily congruent.
Feedback: Correct. Opposite sides and opposite angles in a parallelogram are congruent. Because and are opposite angles in parallelogram RSTQ, they are congruent.
Feedback: Incorrect. Opposite sides and opposite angles in a parallelogram are congruent. Because and are adjacent angles in parallelogram RSTQ, they are not necessarily congruent.
Feedback: Incorrect. Opposite sides and opposite angles in a parallelogram are congruent. Because and are adjacent sides in parallelogram RSTQ, they are not necessarily congruent.

Q: Find the perimeter, in inches, of the parallelogram.
- 40 (Correct. Opposite sides of a parallelogram have the same lengths, so use the formula to find the perimeter.)
- 60 (Incorrect. You multiplied the base of the parallelogram by its height instead of finding the sum of the lengths of the four sides.)
- 20 (Incorrect. You added only the two given side lengths of the parallelogram, but you need to add all four side lengths.)
- 24 (Incorrect. You added the three measurements labeled on the figure, instead of finding the sum of the lengths of the four sides of the parallelogram.)
A: 40

Q: An abstract sculpture in the form of a triangle has a base of 11 meters and a height of 12 meters. Find the area of the triangle.
- 23 square meters (Incorrect. You added the base and the height of the triangle instead of using the formula to find the correct area.)
- 132 square meters (Incorrect. You multiplied the base times the height of the triangle. You need to multiply that product by to find the area.)
- 11.5 square meters (Incorrect. You added the base and the height of the triangle and multiplied the sum by instead of using the formula to find the correct area.)
- 66 square meters (Correct. The formula for the area of a triangle is: Substitute the values and : The area of the triangle is 66 square meters.)
A: 66 square meters

Q: Find the area of the figure below, formed from a triangle and a parallelogram.
- 144 square millimeters (Incorrect. You may have forgotten the in the formula for the area of a triangle.)
- 120 square millimeters (Incorrect. You may have forgotten the in the formula for the area of a triangle and also mistakenly multiplied the area of the parallelogram by , thinking of the formula for a triangle or a trapezoid.)
- 72 square millimeters (Incorrect. You may have mistakenly multiplied the area of the parallelogram by , thinking of the formula for a triangle or a trapezoid.)
- 96 square millimeters (Correct. Add the areas of the triangle and the parallelogram. Area of the triangle: Area of the parallelogram: The total area of the figure is square millimeters.)
A: 96 square millimeters

Q: Which letter on the diagram below represents a radius of the circle?
- D (Incorrect. The letter D represents the circumference of the circle or the circle itself. A radius of a circle is a line segment from the center of the circle to a point on the circle.)
- C (Correct. A radius of a circle is a line segment from the center of the circle to a point on the circle. The line segment labeled with the letter C is a radius.)
- B (Incorrect. The letter B represents a diameter of the circle. A radius of a circle is a line segment from the center of the circle to a point on the circle.)
- A (Incorrect. The letter A represents the center of the circle. A radius of a circle is a line segment from the center of the circle to a point on the circle.)
A: C

Q: Find the circumference of a circle with a diameter of 20 centimeters. Round your answer to the nearest centimeter.
- 6 centimeters (Incorrect. You may have divided the diameter by , instead of multiplying by .)
- 63 centimeters (Correct. The circumference of a circle is given by the formula , with . In this circle, , so: Rounded to the nearest centimeter, the circumference of the circle is 63 centimeters.)
- 126 centimeters (Incorrect. You may have thought that the circumference equals . The formula for the circumference of a circle is or . In this circle, .)
- 31 centimeters (Incorrect. You multiplied by the radius of the circle, instead of multiplying it by the diameter.)
A: 63 centimeters

Q: A flying disc has a radius of 6 inches. What is the area of one side of the flying disc to the nearest square inch? Use 3.14 as an approximation for .
- 38 square inches (Incorrect. You used the formula for the circumference of a circle instead of the area.)
- 28 square inches (Incorrect. You may have thought that the diameter of the flying disc was 6 inches and divided the value by 2 before using the area formula. However, the radius of the flying disc is 6 inches.)
- 113 square inches (Correct. Use in the formula to find the area: Rounded to the nearest square inch, the area of one side of the flying disc is 113 square inches.)
- 452 square inches (Incorrect. You used the square of the diameter in the area formula instead of the square of the radius.)
A: 113 square inches

Q: Find the approximate area of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for .
- 86 square feet (Correct. The diameter of the circle equals the side length of the square. So the area of the square is square feet. Use the radius of the circle, , to find the area of the circle: square feet The area of the shaded region equals the area of the square minus the area of the circle. This is approximately square feet.)
- 214 square feet (Incorrect. After finding and using this to find the area of the circle, you probably used this number as the side length to find the area of the square. Then you subtracted in the wrong order. The side length of the square is 20. Find the area of the square and then subtract the area of the circle from this.)
- 314 square feet (Incorrect. You found the area of the circle. You need to subtract this from the area of the square to find the area of the shaded region.)
- 856 square feet (Incorrect. You probably found the area of the circle using 20 as the radius instead of 10, and then subtracted the area of the square. Find the approximate area of the circle with and then subtract this from the area of the square.)
A: 86 square feet

Q: Which of the following shapes has a circular base?
- cone (Correct. A cone is a solid figure with a single circular base, and a smooth, round face that diminishes to a single point.)
- rectangular prism (Incorrect. A rectangular prism has a rectangular base, not a circular base.)
- pyramid (Incorrect. A pyramid has a polygonal base, not a circular base.)
- cube (Incorrect. A cube has a square base, not a circular base.)
A: cone