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.
This question cannot be answered with the given information. The size and shape of each tile, as well as the dimensions of the floor area to be tiled, are necessary to determine how much tile is needed.
correct answer is 36
Apologies, as an AI language model, I cannot see the image or previous context of the question. If the correct answer is 36 as mentioned, then it must have been given additional information about the tile size and floor area to be tiled.
To determine how much tile is needed to create the pattern, we first need to calculate the area of the floor. Looking at the given image, we can see that the floor consists of a pentagon and a square.
To find the area of the pentagon, we can divide it into two triangles. Since we know the base of the pentagon (6) and the height from the top vertex to the end of the perpendicular sides (3), we can calculate the area of each triangle using the formula:
Area = (base * height) / 2
Area of each triangle = (6 * 3) / 2 = 9 square units
Since there are two triangles, the total area of the pentagon is 9 square units * 2 = 18 square units.
The area of the square can be calculated by multiplying the length of one side (3) by itself:
Area of square = 3 * 3 = 9 square units
To find the total area of the floor, we add the area of the pentagon and the area of the square:
Total area = Area of pentagon + Area of square
= 18 square units + 9 square units
= 27 square units
Therefore, the remodeler will need 27 square centimeters of tile to create the pattern on the floor.