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?
___ square centimeters
To calculate the area of the composite structure, we need to find the area of the pentagon and the square separately, then add them together.
Area of the pentagon:
The base of the pentagon is 6 units long, so the height of the pentagon (from the top vertex to the end of the perpendicular sides) is 3 units. The formula to calculate the area of a pentagon is 1/2 * base * height. Therefore, the area of the pentagon is 1/2 * 6 * 3 = 9 square units.
Area of the square:
The side of the square is 3 units, so the area of the square is side * side = 3 * 3 = 9 square units.
Total area of the composite structure:
Adding the areas of the pentagon and the square together, we get 9 + 9 = 18 square units.
Therefore, the remodeler will need 18 square centimeters of tile to create the pattern on the floor.