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
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To calculate the total area needed for the tile pattern, we need to find the area of the pentagon and the square separately and then add them together.
Area of the pentagon:
The base of the pentagon is 6 and the height is 3 (from the top vertex to the end of the perpendicular sides). The formula for the area of a pentagon is (1/2) * base * height. Plugging in the values, we get (1/2) * 6 * 3 = 9 square units.
Area of the square:
The side of the square is 3, so the area of the square is side * side = 3 * 3 = 9 square units.
Total area needed for the tile pattern:
Adding the area of the pentagon and the square, we get 9 + 9 = 18 square units of tile needed for the pattern.