Secure and Legitimate Architecture Assignment Help for Students

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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.

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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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Question 4:

A landscape architect is designing a rectangular courtyard for a residential complex. The length of the courtyard is 25 meters, and the width is 15 meters. The architect plans to install a grass lawn in the courtyard. If the grass needs to be mowed every two weeks and it takes 4 hours to mow the entire lawn, how many hours will be spent mowing the lawn in a year?

Answer: To find the total number of hours spent mowing the lawn in a year, we need to calculate the number of times the grass needs to be mowed and multiply it by the time taken to mow the lawn each time.

First, let's calculate the area of the lawn: Area of the lawn = length × width Area of the lawn = 25 meters × 15 meters Area of the lawn = 375 square meters

Next, let's calculate the number of times the grass needs to be mowed in a year: Since the grass needs to be mowed every two weeks, there are 52 weeks in a year, so the number of mowings per year is 52 weeks / 2 weeks = 26 mowings.

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Finally, let's calculate the total number of hours spent mowing the lawn in a year:

Total time spent mowing the lawn = number of mowings per year × time taken to mow the lawn each time Total time spent mowing the lawn = 26 mowings × 4 hours per mowing Total time spent mowing the lawn = 104 hours

Therefore, the total number of hours spent mowing the lawn in a year is 104 hours.

Question 5:

A landscape architect is designing a park that includes a circular fountain. The diameter of the fountain is 6 meters. The architect plans to install a circular seating area around the fountain, which extends 2 meters outward from the edge of the fountain. What is the total area of the seating area?

Answer: To find the area of the seating area, we need to calculate the area of the larger circle formed by the outer edge of the seating area and subtract the area of the smaller circle formed by the edge of the fountain.

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Radius of the larger circle = radius of the fountain + width of the seating area

Radius of the larger circle = (6 meters / 2) + 2 meters = 3 meters + 2 meters = 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 fountain Radius of the smaller circle = 6 meters / 2 = 3 meters

Area of the smaller circle = π × (radius of the smaller circle)² Area of the smaller circle = π × (3 meters)² ≈ 28.27 square meters

Therefore, the area of the seating area is 78.54 square meters - 28.27 square meters = 50.27 square meters.

So, the total area of the seating area is approximately 50.27 square meters.

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