Question

At a craft shop, a painter decided to paint a welcome sign to take home. An image of the sign is shown. A five-sided figure with a flat top labeled 5 and one-half feet. A height labeled 4 feet. The length of the entire image is 9 ft. There is a point coming out of the right side of the image that is created by two line segments. What is the area of the sign? 19 square feet 22 square feet 29 square feet 36 square feet Question 2(Multiple Choice Worth 2 points) (Volume of Rectangular Prisms MC) A family is building a sandbox for their yard that is shaped like a rectangular prism. They would like for the box to have a volume of 43,972.5 in3. If they already have the length measured at 71.5 inches and the width at 60 inches, what is the height needed to reach the desired volume? 5.25 inches 10.25 inches 131.5 inches 283.5 inches Question 3(Multiple Choice Worth 2 points) (Perimeter and Area on the Coordinate Plane MC) An office manager needs to cover the front face of a rectangular box with a label for shipping. The vertices of the face are (–8, 4), (4, 4), (–8, –2), and (4, –2). What is the area, in square inches, of the label needed to cover the face of the box? 18 in2 36 in2 60 in2 72 in2 Question 4(Multiple Choice Worth 2 points) (Perimeter and Area on the Coordinate Plane MC) The vertices of a rectangle are plotted in the image shown. A graph with the x-axis and y-axis labeled and starting at negative 8, with tick marks every one unit up to positive 8. There are four points plotted at negative 2, 6, then 3, 6, then negative 2, negative 3, and at 3, negative 3. What is the perimeter of the rectangle created by the points? 14 units 19 units 28 units 45 units Question 5(Multiple Choice Worth 2 points) (Volume of Rectangular Prisms MC) What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards? seven hundred ninety-five and one-fifth yd3 seven hundred thirty-nine and one-fifth yd3 four hundred fifty-two and four

Answer 1

The area of the sign can be calculated by finding the area of the trapezoid shape. The formula for the area of a trapezoid is A = (1/2) * (base1 + base2) * height. In this case, the bases are 5.5 feet (half of 11 feet, which is the flat top of the five-sided figure) and 9 feet (the entire length of the image), and the height is 4 feet. Plugging these values into the formula, we get:

A = (1/2) * (5.5 + 9) * 4

A = (1/2) * 14.5 * 4

A = 7.25 * 4

A = 29

So, the area of the sign is 29 square feet.

The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the length is given as 71.5 inches, the width is given as 60 inches, and the volume is given as 43,972.5 in^3. We can solve for the height by dividing the volume by the product of the length and width:

Height = Volume / (Length * Width)

Height = 43,972.5 / (71.5 * 60)

Height ≈ 10.25 inches

So, the height needed to reach the desired volume is approximately 10.25 inches.

The area of the rectangular box face can be calculated by finding the length of the sides of the rectangle using the given coordinates, and then using the formula for the area of a rectangle, which is A = length * width. In this case, the length is the difference between the x-coordinates of the two points on the x-axis (4 - (-8) = 12) and the width is the difference between the y-coordinates of the two points on the y-axis (4 - (-2) = 6). Plugging these values into the formula, we get:

A = 12 * 6

A = 72

So, the area of the label needed to cover the face of the box is 72 square inches.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, we can use the given coordinates of the four points to find the lengths of the sides. The length is the difference between the x-coordinates of the two points on the x-axis (3 - (-2) = 5) and the width is the difference between the y-coordinates of the two points on the y-axis (6 - (-3) = 9). Since the opposite sides of a rectangle have equal lengths, the perimeter is twice the sum of the length and width:

Perimeter = 2 * (Length + Width)

Perimeter = 2 * (5 + 9)

Perimeter = 2 * 14

Perimeter = 28

So, the perimeter of the rectangle created by the points is 28 units.

The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the length is given as 14.2 yards (14 and one-fifth yards), the width is given as 7 yards, and the height is given as 8 yards. Plugging these values into the formula, we get:

Volume = Length * Width * Height

Volume = 14.2 * 7 * 8

Volume ≈ 795.2

So, the volume of the rectangular prism is approximately 795.2 cubic yards. Answer: seven hundred ninety-five and one-fifth yd3