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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page 15 of 17
To calculate the area of the tile pattern needed, first calculate the area of the pentagon and the area of the square, then add them together.
The area of the pentagon can be divided into a rectangle (base of the pentagon with length 6 and height of 3) and a triangle (with base of 3 and height of 3).
Area of rectangle = base x height = 6 x 3 = 18
Area of triangle = 0.5 x base x height = 0.5 x 3 x 3 = 4.5
So, area of the pentagon = Area of rectangle + Area of triangle = 18 + 4.5 = 22.5 square units
The area of the square is simply side x side = 3 x 3 = 9 square units.
Therefore, the total tile needed for the pattern is 22.5 + 9 = 31.5 square units.