### Brain Teasers

# Patio Plans

Jill is helping plan her family's new patio. It will be an irregular hexagon. They will use 1-foot-square stone tiles. Here are her notes.

1. The perimeter of the deck is outlined by ABCDEF.

2. Line AB is against the house. It is 16 feet long.

3. AF is perpendicular to AB.

4.AF and BC are parallel.

5.BC and AF are each 6 feet long.

6.Points F and C are connected by FC; FC is parallel to AB.

7.Points G and H are on FC.

8.FG and HC are each 4 feet long.

9. ED is 8 feet long. It is parallel to AB.

10. DH is perpendicular to HC. It is 4 feet long.

11. EG is perpendicular to FG. It is 4 feet long.

12. Angle BCD is 135 degrees.

13. Angle AFE is 135 degrees.

If they order 6 more tiles than they would ideally need (to allow for breakage), how many patio tiles should they order?

Assume that tiles can be cut cleanly so that any leftover pieces can be used for other parts of the deck.

1. The perimeter of the deck is outlined by ABCDEF.

2. Line AB is against the house. It is 16 feet long.

3. AF is perpendicular to AB.

4.AF and BC are parallel.

5.BC and AF are each 6 feet long.

6.Points F and C are connected by FC; FC is parallel to AB.

7.Points G and H are on FC.

8.FG and HC are each 4 feet long.

9. ED is 8 feet long. It is parallel to AB.

10. DH is perpendicular to HC. It is 4 feet long.

11. EG is perpendicular to FG. It is 4 feet long.

12. Angle BCD is 135 degrees.

13. Angle AFE is 135 degrees.

If they order 6 more tiles than they would ideally need (to allow for breakage), how many patio tiles should they order?

Assume that tiles can be cut cleanly so that any leftover pieces can be used for other parts of the deck.

### Answer

The area of the deck is 144 square feet. They will need 150 tiles.Explanation

The area of ABCF is 96 square feet.

The area of DEGH is 32 square feet.

The area of CDH and EFG combined is 16 square feet. You will be able to complete these sections with 8 tiles each after cutting four of the tiles in half diagonally.

The total area is 144 square feet. Allowing 6 extra tiles for breakage brings the order to 150 tiles.

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