Question

liz is installing a tile backsplash. if each tile is an equilateral triangle with sides that measures 6 cm in length how many tiles does she need to cover an area of 1800 cm²

Answer 1

100 tiles

Explanation:

Each tile is an equilateral triangle with sides 6 cm in length, so the area of each tile can be found using the formula for the area of a triangle:

`\sf:\implies{A = (b * h) / 2}`

where b is the base and h is the height.

Since each side of the triangle is 6 cm, the base and height of the triangle are both 6 cm, so:

`\sf:\implies{A = (b * h) / 2}`

`\sf:\implies{A = (6 * 6) / 2}`

`\sf:\implies{A =18}`

So each tile has an area of 18 cm².

To find the number of tiles needed to cover an area of 1800 cm², divide the total area by the area of each tile:

`\sf:\implies{A = 1800 / 18}`

`\sf:\implies{A = 100}`

Therefore, Liz needs 100 tiles to cover an area of 1800 cm².

Answer 2

116 tiles

Explanation:

You want to know the number of 6 cm equilateral triangle tiles required to cover 1800 cm².

Area

The area of an equilateral triangle of side s is given by the formula ...

A = (√3/4)s²

The area of a 6 cm equilateral triangle tile is ...

A = (√3/4)(6 cm²) = 9√3 cm² ≈ 15.588 cm²

Tiles

The number of tiles required is the total area divided by the area per tile:

1800 cm² / (15.588 cm²/tile) ≈ 115.47 tiles

In order to cover 1800 cm², Liz will need 116 triangular tiles.