Use Area to Solve Problems Practice
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5 of 55 of 5 Items
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Question
Use the image to answer the question.
An illustration shows a composite structure of a pentagon with two right angles and a square, resembling a house. The base of the pentagon is of length 6. The two sides are perpendicular to the base. The perpendicular right side of the pentagon shares a common side with a square of side 3, with the base of the square continuing out length 3 from the end of the pentagon base of length 6. A solid vertical line is drawn from the top vertex of the pentagon to the midpoint on the base, dividing the shape in half. The height from the top vertex to the end of the perpendicular sides is marked as 3.
A home remodeler has chosen a tile pattern for a floor. How much tile is needed to create the pattern?
(1 point)
square centimeters
To find the total area of the composite structure, we first need to find the area of the pentagon and the square separately.
The area of the pentagon can be found using the formula: Area = 1/2 * base * height
Area = 1/2 * 6 * 3 = 9 square units
The area of the square is calculated as: Area = side * side
Area = 3 * 3 = 9 square units
Adding the areas of the pentagon and the square together, we can find the total area:
Total Area = 9 + 9 = 18 square units
Therefore, the home remodeler would need 18 square units of tile to create the pattern.
wrong
I apologize for the mistake in my previous calculation.
To determine the total area of the composite structure, we need to add the areas of the pentagon and the square together.
The area of the pentagon is calculated as: Area = (base * height) / 2
Area = (6 * 3) / 2 = 9 square units
The area of the square is found by squaring the length of one side: Area = side * side
Area = 3 * 3 = 9 square units
Adding the areas of the pentagon and the square yields the total area:
Total Area = 9 + 9 = 18 square units
Therefore, the home remodeler would need 18 square units of tile to create the pattern.
wrong you not even trying
I apologize for the confusion. Let's try to solve the problem correctly this time.
To find the total area of the composite structure, we should calculate the area of the pentagon and the square separately, and then add the two areas together.
1. Calculating the area of the pentagon:
The pentagon is divided into two parts - a triangle and a rectangle. We can find the areas of these two parts separately and then add them together.
Area of the triangle = (base * height) / 2
Area of the triangle = (6 * 3) / 2 = 9 square units
Area of the rectangle = base * height
Area of the rectangle = 6 * 3 = 18 square units
Total area of the pentagon = Area of triangle + Area of rectangle = 9 + 18 = 27 square units
2. Calculating the area of the square:
The area of the square is calculated as: Area = side * side
Area of the square = 3 * 3 = 9 square units
Now, we can find the total area of the composite structure by adding the area of the pentagon and the square:
Total Area = Area of pentagon + Area of square = 27 + 9 = 36 square units
Therefore, the home remodeler would need 36 square units of tile to create the pattern.
correct
Thank you for confirming that the correct answer is 36 square units. If you have any more questions or need further assistance, feel free to ask!
i think you are ready for harder ones first one is
Use Area to Solve Problems Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the question.
An illustration shows a trapezoid with shorter base of length 36 and the opposite longer side of length 48. The legs on the left and right sides are of length 21. The perpendicular height from the bottom left vertex to the longer side is 18. The length between the top left vertex of the longer side and the point where the height meets the longer side is labeled 6. The height is shown in a dashed line.
Compose a rectangle to help find the area of a trapezoid-shaped tabletop in square inches. What is the area of the tabletop?
(1 point)
Responses
756 square inches
756 square inches
648 square inches
648 square inches
882 square inches
882 square inches
864 square inches
To find the area of the trapezoid-shaped tabletop, we can add a rectangle to it to form a parallelogram. The base of the parallelogram is the sum of the shorter base of the trapezoid (36) and the length from the top left vertex to the point where the height meets the longer side (6), which is 36 + 6 = 42. The height of the parallelogram is the same as the height of the trapezoid, which is 18.
First, we find the area of the parallelogram:
Area = base * height
Area = 42 * 18
Area = 756 square inches
Therefore, the area of the trapezoid-shaped tabletop is 756 square inches.
number two
Use Area to Solve Problems Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration shows a parallelogram that is divided into four equal sections by a horizontal and a vertical line intersecting at the center. Measurements are labeled on the bottom first section as follows: The base is labeled 8 inches and left side is 5 inches. The perpendicular height from the top left vertex to the base is 4 inches. The height is drawn in dashed line.
To cover a garden path, a landscape designer plans to cover a walkway with parallelogram-shaped paving stones. Construct a rectangle to find the area covered by 4 paving stones. What is the area in square inches?
(1 point)
Responses
52 square inches
52 square inches
160 square inches
160 square inches
128 square inches
128 square inches
40 square inches