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 how much tile is needed to create the pattern, we need to calculate the total area of the shape formed by the pentagon and the square.
The pentagon has a base of length 6 and a height of 3, making it a right triangle with area = 0.5 * base * height = 0.5 * 6 * 3 = 9 square units.
The square has a side length of 3, so its area is side^2 = 3^2 = 9 square units.
Therefore, the total area of the shape is 9 (pentagon area) + 9 (square area) = 18 square units.
So, the remodeler would need 18 square centimeters of tile to create the pattern.
no
To find the total area of the shape formed by the pentagon and the square, we need to calculate the areas of each shape separately and then add them together.
The pentagon has a base of length 6 and a height of 3, making it a right triangle with area = 0.5 * base * height = 0.5 * 6 * 3 = 9 square units.
The square has a side length of 3, so its area is side^2 = 3^2 = 9 square units.
Therefore, the total area of the shape is 9 (pentagon area) + 9 (square area) = 18 square units.
So, the remodeler would need 18 square centimeters of tile to create the pattern.
wrong
Apologies for the previous incorrect response. Let's try solving the problem again.
To find the total area of the shape, we can break it down into two parts: the pentagon and the square.
1. Area of the pentagon:
The pentagon is essentially a triangle with a base of length 6 and a height of 3.
Area of triangle = 0.5 * base * height
Area of pentagon = 0.5 * 6 * 3 = 9 square units
2. Area of the square:
The square has a side length of 3.
Area of square = side^2 = 3^2 = 9 square units
Now, to find the total area of the shape, we add the areas of the pentagon and the square:
Total area = 9 (pentagon area) + 9 (square area) = 18 square units
Therefore, the remodeler would need 18 square units of tile to create the pattern.