Question

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 5 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 5 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?

53 cm2
45.5 cm2
42.5 cm2
36.5 cm2

Answer 1

To find the area of the tile, we need to first find the length of the top horizontal side.

Using the Pythagorean theorem, we can find the length of the diagonal:

d² = 3² + (5+6)²

d² = 9 + 121

d = √130

Now we can use the fact that the diagonal cuts the rectangle into two right triangles to find the length of the top horizontal side:

5x = 3(6)

x = 18/5

Therefore, the length of the top horizontal side is 18/5 centimeters.

Now we can find the area of the tile:

A = (3 + 18/5) * 5/2

A = 15 + 27/5

A = 102/5

Rounding to one decimal place, we get:

A ≈ 20.4 cm²

Therefore, the closest option to the area of the tile shown is 42.5 cm².