A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 7 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 4 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.
What is the area of the tile shown?
58 cm2
44 cm2
74 cm2
70 cm2
To find the area of the tile, we can split it into two triangles and one rectangle.
The area of the rectangle is the base times the height, so it is 6 cm x 3 cm = 18 cm^2.
The area of the larger triangle is (b x h)/2, so it is (4 cm x 7 cm)/2 = 14 cm^2.
The area of the smaller triangle is (b x h)/2, so it is (2 cm x 3 cm)/2 = 3 cm^2.
Adding up the areas of the rectangle and the two triangles, we get 18 cm^2 + 14 cm^2 + 3 cm^2 = 35 cm^2.
Therefore, the area of the tile shown is 35 cm^2.