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Exam 25: Counting Units Fast: Measurement Formulas

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Question 1

Essay

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Find an expression for the area of the figure below, in terms of the indicated measurements. (Angles that look like right angles are right angles.)

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Question 2

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What is the area of the triangle below in square centimeters? The given measurements are in centimeters.

A) 32
B) 31
C) 24
D) 16
E) None of the answers is correct.

F) None of the above
G) A) and C)

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Question 3

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You would like to buy wheels for your child's go-cart so that the wheels will roll 1 meter in one full revolution. What should the diameter of each wheel be in meters?

Give the area and the perimeter of the following shape. The curved edges are semicircles with the indicated points as centers.

To the nearest inch, a rectangle measures 2 inches by 4 inches. The area of the rectangle could be anywhere between _____ square inches and _____ square inches. Please express your answer(s) as fractions or mixed numbers.

What is the area of the circle below?

What is the volume of the box below? Height of box $= 2.5$ inches Area of bottom of box $= 35 \mathrm { sq }$ . inches Length of diagonal of bottom $= 8.5$ inches

What is the area of a rectangle similar to the one shown with a size change of scale factor 4?

Explain why a formula for the area of a trapezoid is the following. A_trap = $\frac { 1 } { 2 } \left( \text { Base } _ { 1 } + \text { Base } _ { 2 } \right) ( \text { height } )$

Find the area of the triangle.

Explain why a formula for the volume of a prism is the following. (Use a drawing if that is helpful.) V_prism = (area of the base)(height)

A) Sketch the three-dimensional shape that has the net shown. (The middle part is a rectangle.) B) Name the three-dimensional shape as fully as possible. C) Give the volume and surface area of the three-dimensional shape. (Use correct units. Show your work for credit.)

In the shape below, ABCDE is a regular pentagon, M is the midpoint of side AB, and A is the center of the circular arc. Find the area of the shaded shape and the perimeter of the entire shape.

If the diameter of a tennis ball is a little more than 6 centimeters, what is the approximate surface area and volume of the tennis ball?

You would like to buy wheels for your child's go-cart, so that the wheels will roll 1 meter in one full revolution. What should the diameter of each wheel be in centimeters?

Find the area of the figure, if c = 8 cm, n = 7 cm, and a = 20 cm. (Angles that look like right angles are right angles.)

The lengths of the sides of the triangle below are x, y, and z, and with p as shown. Tell how to use the figure to justify the formula for the area of the triangle, without introducing any new variables. Write enough to make your thinking clear.

The area of the triangle below is 24 square units. Each of the sides in a triangle can be used as a base. For each of the triangles shown, choose a different side as the base and then draw the corresponding height for that base. Find the measurement of that height.

The perimeter of a square is 20 centimeters. What is its area in square centimeters?

What is the area of a rectangle with perimeter 20 meters and base 6 meters?