To find the area of the hexagonal shape made up of equilateral triangles with side length 7 cm, we first need to find the area of one equilateral triangle.
The formula for the area of an equilateral triangle is:
Area = (sqrt(3) / 4) * s^2
where s is the length of the side of the equilateral triangle.
Plugging in s = 7 cm, we get:
Area = (sqrt(3) / 4) * 7^2
Area = (sqrt(3) / 4) * 49
Area = (7sqrt(3)) / 4
Area ≈ 12.02 cm^2
Since each hexagonal shape is made up of six equilateral triangles, the area of the hexagonal shape would be:
Area = 6 * 12.02 cm^2
Area = 72.12 cm^2
Therefore, the exact area of each hexagonal shape is approximately 72.12 cm^2.
You are planning to use a
ceramic tile design in your
new bathroom. The tiles are
equilateral triangles. You
decide to arrange the tiles in a
hexagonal shape as shown.
If the side of each tile
measures 7 cm, what will be
the exact area of each
hexagonal shape?
(1 point)
73.5 cm2
98 cm2
21 cm2
1029 cm2
3 answers
An answer from the choices
To find the area of each hexagonal shape, we can divide the shape into six equilateral triangles. Each equilateral triangle will have side length of 7 cm.
The formula for the area of an equilateral triangle is: Area = (√3 / 4) * s^2, where s is the side length.
Plugging in s = 7 cm, we get: Area = (√3 / 4) * 7^2 = (√3 / 4) * 49 = 49√3 / 4
Since there are six equilateral triangles in the hexagon, the total area of the hexagon is 6 * (49√3 / 4) = 294√3 / 4 ≈ 127.3 cm^2
So, the closest answer from the choices provided is 98 cm^2.
The formula for the area of an equilateral triangle is: Area = (√3 / 4) * s^2, where s is the side length.
Plugging in s = 7 cm, we get: Area = (√3 / 4) * 7^2 = (√3 / 4) * 49 = 49√3 / 4
Since there are six equilateral triangles in the hexagon, the total area of the hexagon is 6 * (49√3 / 4) = 294√3 / 4 ≈ 127.3 cm^2
So, the closest answer from the choices provided is 98 cm^2.