Use Area to Solve Problems Practice
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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 needed for the tile pattern, we need to calculate the individual areas of the pentagon and the square within the composite structure.
The area of the pentagon can be calculated using the formula: (1/2) * base * height
= (1/2) * 6 * 3
= 9 square units
The area of the square can be calculated as side * side
= 3 * 3
= 9 square units
Therefore, the total area needed for the tile pattern is:
9 square units (pentagon) + 9 square units (square) = 18 square units
So, the remodeler needs 18 square centimeters of tile to create the pattern.