Answer:
(a) 7000 square feet
(b) Three and a half bags.
Step-by-step explanation:
Given:
A green lawn in the shape of a trapezium surrounds a rectangular office building.
(a)
The area of the green lawn can be calculated by subtracting the area of the office building from the total area of the trapezoidal lawn and building.
Let us find each areas.
Area of trapezium = [tex]\frac{1}{2}\times(Sum\ of\ parallel\ sides)\times Height[/tex]
Area of trapezium = [tex]0.5\times (100+140)\times 80[/tex]
Area of trapezium = 40 × 240 = 9600 square feet
Now, area of rectangular building is given as:
Area of building = Length × Width
Area of building = 50 × 52 = 2600 square feet
Now, area of lawn is given as:
Lawn area = Trapezium area - Building area
Lawn area = 9600 - 2600 = 7000 square feet.
(b)
Given:
1 bag of seeds cover 2000 square feet lawn area.
Let, 'x' bags cover the total lawn area of 7000 square feet.
Setting up a proportion and solving by cross multiplication method, we get:
[tex]\frac{1}{2000}=\frac{x}{7000}\\\\2000x=7000\\\\x=\frac{7000}{2000}=3.5=3\frac{1}{2}[/tex]
Therefore, the number of bags of seeds required to cover 7000 square feet of lawn is three and a half.
