To find the area of the shape in square inches, we need to find the areas of each of the simple polygons that make up the box net and add them together.
Starting with the rectangle at the center, we can find its area by multiplying the length and width:
Area of rectangle = length x width = (3+3+6) x (6+3+3) = 36 square inches
Next, we can find the area of each of the trapezoids. The trapezoid on the left has a height of 6 (the width of the rectangle) and bases of 3 and 1.2:
Area of left trapezoid = (3 + 1.2) / 2 x 6 = 13.2 square inches
The two trapezoids on the top and bottom have a height of 3 (the width of the squares) and bases of 3 and 6:
Area of each top/bottom trapezoid = (3 + 6) / 2 x 3 = 13.5 square inches
Finally, we can find the area of each of the squares by squaring their side lengths of 3:
Area of each square = 3 x 3 = 9 square inches
Adding up all the areas, we get:
36 + 13.2 + 2(13.5) + 2(9) = 94.2 square inches
Therefore, we need 94.2 square inches of cardboard to make the cube.
Use the image to answer the question.
An illustration shows an unfolded box net. It is comprised of a rectangle at the center, two squares extending into three trapezoids on the top and bottom, and a trapezoid on the left of the rectangle. The top side of the rectangle is labeled in three distinct sections: starting at the left, a solid line of 3 is drawn, followed by a dashed line of 3, and then a solid line of 6. The bottom of the rectangle is labeled in three distinct sections: a solid line of 6, a dashed line of 3, and a solid line of 3. The left width of the rectangle is drawn as a dashed line, labeled as 3, which becomes the base of a shaded trapezoid. The dashed lines on the top and bottom of the rectangle are extended into squares of side 3, sides drawn in dashed lines. The three outer sides of each square become the longer bases of shaded trapezoids. The top shorter side of the trapezoid is labeled as 1.2 and the perpendicular height is 1.
Decompose the box net into simple polygons to find how much cardboard in square inches is needed to make the cube. Assume that all angles that look like right angles are right angles. All polygons that look congruent are congruent. What is the area of the shape in square inches?
15 answers
Which of the following is the best way to reduce the need for additional energy consumption?
a
remediation
b
preservation
c
reservation
d
conservation
a
remediation
b
preservation
c
reservation
d
conservation
d. conservation
Jenny is trying to help her family conserve electricity. Which of the following would be the best way for Jenny to help her family do this?
a
Jenny should turn off her computer when she is not using it.
b
Jenny should only buy clothes that are made from natural resources.
c
Jenny should recycle plastic and glass bottles after she is done using them.
d
Jenny should set the air conditioner in her home to a much colder temperature.
a
Jenny should turn off her computer when she is not using it.
b
Jenny should only buy clothes that are made from natural resources.
c
Jenny should recycle plastic and glass bottles after she is done using them.
d
Jenny should set the air conditioner in her home to a much colder temperature.
a. Jenny should turn off her computer when she is not using it.
Rare earth metals are rarely found in large quantities on Earth. Instead, they are spread very thinly throughout Earth's crust, making them very difficult to get. Once they are all used, they are gone forever. Which energy resource is similar to rare Earth metals in that once it is used up, it is gone?
a
wood
b
solar
c
wind
d
oil
a
wood
b
solar
c
wind
d
oil
d. oil
Which of the following best explains why conserving resources is important?
a
There are a limited amount of resources on Earth, so conserving them will make them last longer.
b
Humans need to learn how to make the resources faster, so conserving them gives them a chance to learn how.
c
There are too many resources on Earth, so conserving them helps to create more space for humans to build cities.
d
Humans require resources, so conserving them helps make sure they are replaced when they are used.
a
There are a limited amount of resources on Earth, so conserving them will make them last longer.
b
Humans need to learn how to make the resources faster, so conserving them gives them a chance to learn how.
c
There are too many resources on Earth, so conserving them helps to create more space for humans to build cities.
d
Humans require resources, so conserving them helps make sure they are replaced when they are used.
a. There are a limited amount of resources on Earth, so conserving them will make them last longer.
What would be the best question to ask in order to immediately determine whether or not an energy resource is renewable?
a
How long until it runs out?
b
How many people use it?
c
How much energy does it produce?
d
How long has it been used?
a
How long until it runs out?
b
How many people use it?
c
How much energy does it produce?
d
How long has it been used?
a. How long until it runs out?
Georgia has a lot of potential to produce power from renewable resources. About two-thirds of Georgia is forested. What type of renewable resource could Georgia most likely produce from the forests?
a
Biomass
b
Hydroelectric
c
Geothermal
d
Wind Energy
a
Biomass
b
Hydroelectric
c
Geothermal
d
Wind Energy
a. Biomass
Which of the following is a nonrenewable source of energy?
a
energy from the Sun
b
wind energy
c
geothermal energy
d
energy from burning coal
a
energy from the Sun
b
wind energy
c
geothermal energy
d
energy from burning coal
d. energy from burning coal
1 answer