To calculate the amount of tile needed, we need to calculate the total area of the shape.
First, we calculate the area of the pentagon. The formula for the area of a regular pentagon is (1/4) * (5 * s) * h, where s is the length of a side and h is the height. In this case, s = 6 and h = 3. So, the area of the pentagon is (1/4) * (5 * 6) * 3 = 22.5 square units.
Next, we calculate the area of the square. Since the side length is 3, the area of the square is 3 * 3 = 9 square units.
Adding the areas of the pentagon and square together, we get 22.5 + 9 = 31.5 square units.
Therefore, the home remodeler will need 31.5 square units of tile to create the pattern.
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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5 answers
square centimeters
To convert square units to square centimeters, we need to multiply by a conversion factor.
Since 1 square unit is equal to 100 square centimeters, we can multiply 31.5 square units by 100 to get the area in square centimeters:
31.5 square units * 100 = 3150 square centimeters
Therefore, the home remodeler will need 3150 square centimeters of tile to create the pattern.
Since 1 square unit is equal to 100 square centimeters, we can multiply 31.5 square units by 100 to get the area in square centimeters:
31.5 square units * 100 = 3150 square centimeters
Therefore, the home remodeler will need 3150 square centimeters of tile to create the pattern.
no
I apologize for the mistake. Let's correct that.
Given that the length of the pentagon's base is 6 units and the height is 3 units, we can calculate the area of the pentagon using the formula for the area of a trapezoid: Area = ((a+b)/2) * h, where a and b are the lengths of the two parallel sides and h is the height.
The pentagon can be divided into a triangle and a rectangle. The base of the triangle is 6 units, and its height is 3 units. Hence, the area of the triangle is (1/2) * base * height = (1/2) * 6 * 3 = 9 square units.
The rectangle portion of the pentagon has a base of 3 units and a height of 3 units. Therefore, the area of the rectangle is 3 * 3 = 9 square units.
Adding the areas of the triangle and the rectangle together, we get 9 + 9 = 18 square units.
Therefore, the home remodeler will need 18 square units of tile to create the pattern.
Given that the length of the pentagon's base is 6 units and the height is 3 units, we can calculate the area of the pentagon using the formula for the area of a trapezoid: Area = ((a+b)/2) * h, where a and b are the lengths of the two parallel sides and h is the height.
The pentagon can be divided into a triangle and a rectangle. The base of the triangle is 6 units, and its height is 3 units. Hence, the area of the triangle is (1/2) * base * height = (1/2) * 6 * 3 = 9 square units.
The rectangle portion of the pentagon has a base of 3 units and a height of 3 units. Therefore, the area of the rectangle is 3 * 3 = 9 square units.
Adding the areas of the triangle and the rectangle together, we get 9 + 9 = 18 square units.
Therefore, the home remodeler will need 18 square units of tile to create the pattern.