Area and Volume Unit Test
6 of 156 of 15 Items
Question
Use the image to answer the question.
An illustration of a parallelogram shows the following dimensions: The base is 12 feet. The perpendicular height from the top left vertex to the base is 7 inches. The height is drawn as a dashed line.
A pool company is installing a parallelogram-shaped swimming pool in a family’s back yard. Compose a rectangle to find the amount of area that the pool will take up in the yard. What is the area of the pool?
(1 point)
square feet
The area of the parallelogram-shaped swimming pool can be found by multiplying the base by the perpendicular height.
Base = 12 feet = 144 inches
Perpendicular height = 7 inches
Area = 144 inches * 7 inches = 1008 square inches
To convert square inches to square feet, divide by 144.
1008 square inches / 144 = 7 square feet
Therefore, the area of the pool is 7 square feet.
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?
(1 point)
square inches
To find the area of the shape in square inches, we need to decompose the box net into simple polygons.
Since the details of the shape are not mentioned, it is difficult to determine the exact polygons. However, to calculate the total area, we need to determine the area of each polygon within the net and sum them up.
After decomposing the net into simple polygons, find the area of each polygon and add them together to get the total area in square inches.
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?
(1 point)
_ square inches
To calculate the total surface area of the cube, we need to decompose the box net into simple polygons.
A cube has 6 faces, all of which are squares:
1. There are 3 squares on the outside, which are the faces of the cube.
2. There are 3 squares that make up the inside.
3. These 3 inside squares can be folded to form the faces of the cube.
Therefore, the total surface area of the cube is the summation of the areas of these 6 squares.
Let's denote the side length of the cube as 's'. The area of one square face of the cube is s * s = s^2.
Since there are 6 faces, the total surface area of the cube is:
6 * s^2 = 6s^2 square units.
However, without knowing the length of the side 's', we cannot calculate the exact area in square inches. Please provide the length of the side of the cube so we can calculate the total area in square inches.
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?
(1 point)
_____ square inches
Since we are dealing with a cube, we know that a cube has 6 faces, all of which are squares.
To calculate the total surface area of the cube, we need to consider each face of the cube.
When we unfold a cube net, we will see 6 squares. To calculate the total area of the shape in square inches, we need to sum up the areas of these 6 squares.
Let's say each side of the cube has a length of "s".
The area of one square face of the cube is s * s = s^2.
Since there are 6 faces, the total surface area of the cube is 6 * s^2 = 6s^2 square inches.
Therefore, the area of the shape in square inches is 6s^2 square inches.
An artist is planning to paint an arrow using the pattern shown. What is the amount of area in square feet that will be painted?
(1 point)
square feet
To find the amount of area in square feet that will be painted for the given arrow pattern, we need to break down the shape into simple geometric figures.
The arrow pattern consists of a rectangle and two right-angled triangles.
Let's start by calculating the area of each component:
1. Rectangle:
The dimensions of the rectangle are not given, but we see that the long side of the rectangle is 5 units long. Let's assume the width of the rectangle is 2 units.
Area of rectangle = length * width
Area of rectangle = 5 units * 2 units
Area of rectangle = 10 square units
2. Triangles:
Since the triangles are right-angled, we can use the formula for the area of a triangle:
Area of triangle = 0.5 * base * height
For each triangle:
Area of triangle = 0.5 * (2 units) * (5 units) = 5 square units
There are two triangles, so the total area of both triangles = 2 * 5 = 10 square units
Now, sum up the areas of the rectangle and the triangles:
Total area painted = Area of rectangle + Area of triangles
Total area painted = 10 square units + 10 square units
Total area painted = 20 square units
To convert square units to square feet, we need to know the scale or size relation mentioned in the question. Once we have the scale or size information, we can convert the area into square feet.