


Question 1:
A landscape architect is designing a rectangular garden with a length of 20 meters and a width of 15 meters. The client wants to install a pathway that runs diagonally across the garden from one corner to the opposite corner. The width of the pathway is 1 meter. What is the total area of the pathway?
Answer: To find the area of the pathway, we need to calculate the area of the rectangle and subtract the area of the garden without the pathway.
Area of the rectangle = length × width Area of the rectangle = 20 meters × 15 meters = 300 square meters

To find the area of the garden without the pathway, we need to subtract the area of the triangular regions formed by the pathway from the area of the rectangle.
The pathway divides the rectangle into two congruent right triangles. The base and height of each triangle are the width and length of the pathway, respectively.


Area of one triangular region = (1 meter × 20 meters) / 2 = 10 square meters


Since there are two triangular regions, the total area of the triangular regions is 2 × 10 square meters = 20 square meters.
Therefore, the area of the pathway is 300 square meters - 20 square meters = 280 square meters.
So, the total area of the pathway is 280 square meters.
Question 2:
A landscape architect is designing a circular pond in a garden. The diameter of the pond is 8 meters. The architect wants to install a decorative stone border around the pond, which extends 1 meter outward from the edge of the pond. What is the total area of the stone border?
Answer: To find the area of the stone border, we need to calculate the area of the larger circle formed by the outer edge of the stone border and subtract the area of the smaller circle formed by the edge of the pond.
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Radius of the larger circle = radius of the pond + width of the stone border Radius of the larger circle = (8 meters / 2) + 1 meter = 4 meters + 1 meter = 5 meters
Area of the larger circle = π × (radius of the larger circle)² Area of the larger circle = π × (5 meters)² ≈ 78.54 square meters


Radius of the smaller circle = radius of the pond Radius of the smaller circle = 8 meters / 2 = 4 meters
Area of the smaller circle = π × (radius of the smaller circle)² Area of the smaller circle = π × (4 meters)² ≈ 50.27 square meters
Therefore, the area of the stone border is 78.54 square meters - 50.27 square meters = 28.27 square meters.
So, the total area of the stone border is approximately 28.27 square meters.
Question 3: A landscape architect is designing a triangular park with the following dimensions: Side 1: 30 meters Side 2: 40 meters Side 3: 50 meters
The architect wants to install a walkway that covers 10% of the park's total area. What is the area of the walkway?
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Answer: To find the area of the walkway, we first need to calculate the total area of the triangular park, and then find 10% of that area.
Using Heron's formula, we can find the area of the triangular park:
Semi-perimeter (s) = (Side 1 + Side 2 + Side 3) / 2 Semi-perimeter (s) = (30 meters + 40 meters + 50 meters) / 2 Semi-perimeter (s) = 120 meters / 2 Semi-perimeter (s) = 60 meters
Area of the triangular park = √(s × (s - Side 1) × (s - Side 2) × (s - Side 3)) Area of the triangular park = √(60 meters × (60 meters - 30 meters) × (60 meters - 40 meters) × (60 meters - 50 meters)) Area of the triangular park ≈ √(60 meters × 30 meters × 20 meters × 10 meters) Area of the triangular park ≈ √(3,600,000) ≈ 1897.37 square meters
Now, we can find 10% of the area of the triangular park to determine the area of the walkway:
Area of the walkway = 0.1 × Area of the triangular park Area of the walkway = 0.1 × 1897.37 square meters Area of the walkway ≈ 189.737 square meters


Therefore, the area of the walkway is approximately 189.737 square meters.
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