Question

Kiana wants to cover an area of her backyard with concrete patio stones in the shape of a

right triangle. Each stone costs $0,42 and covers 29.26 square inches. Each square in the grid
represents 1 square foot. If R(1,1), E (7,9), and D (15,3), what is the minimum number of stones
that Kiana should buy to cover the right triangular area in her backyard? Show your work
below.
E(7,9)
D(15,3)
X2 V2
7,9)
R(1,1)
No

Answer 1

Kiana should purchase a minimum of 279 patio stones to cover the right triangular area formed by the points R(1,1), E(7,9), and D(15,3) in her backyard, with each stone covering 29.26 square inches and each square on the grid representing 1 square foot.

Step-by-step explanation:

To determine the minimum number of stones Kiana should buy to cover the right triangular area in her backyard, we first need to calculate the area of the triangle formed by the points R(1,1), E(7,9), and D(15,3). Since the coordinates correspond to a grid where each square represents 1 square foot, we can find the length of the base and height in feet and then find the area in square feet.

Base (BD) = Distance between D and R = √((15-1)² + (3-1)²) = √(196 + 4) = √200 = 14.14 feet
Height (height from E perpendicular to BD) = 9 - 1 = 8 feet
Area of triangle in square feet (A) = 0.5 × base × height = 0.5 × 14.14 × 8 = 56.56 sq ft

We need to convert this area into square inches because each stone covers 29.26 square inches. There are 144 square inches in a square foot.

Area in square inches (A_in) = 56.56 sq ft × 144 sq in/sq ft = 8144.64 sq in
Number of stones needed = A_in / area covered by one stone = 8144.64 sq in / 29.26 sq in = 278.37

Since we can't buy a fraction of a stone, Kiana needs to purchase at least 279 patio stones to cover the entire triangular area.