Using the floorplan below, calculate the total area of the space. Please show all work.
Answers
Answer:
913.39 square feet
Step-by-step explanation:
To answer this question we need to divide the field into regular shapes.
In the diagram we have rectangles, a trapezium and a semicircle.
1) The semicircle
The radius = (3 × 5) /2 = 7.5 feet
Area = ½ × pie × r² = ½ × 22/7 × 7.5²
= 88.39 square feet.
2) Trapezium
a = 1 × 5 = 5 feet
b = 3 × 5 = 15 feet
h = 1 × 5 = 5 feet
Area = ½(a + b) × h
Area = ½ × (15 + 5) × 5
= 50 square feet.
3) Rectangles
Rectangle 1 : length = 3 × 5 = 15 feet
Width = 2 × 5 = 10 feet
Area = 15 × 10 = 150 square feet.
Rectangle 2: length = 5 × 5 = 25 feet.
Width = 3 × 5 = 15 feet
Area = 25 × 15 = 375 square feet.
Rectangle 3 : Length = 5 × 5 = 25 feet
Width = 2 × 5 = 10 feet
Area = 25 × 10 = 250 square feet.
The total area of the field is therefore :
250 + 375 + 150 + 50 + 88.39 = 913.39 square feet.