Question

Use the diagram that shows the lawn that surrounds an office building.​

Answer 1

(a) 7000 square feet

(b) Three and a half bags.

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 =
`(1)/(2)*(Sum\ of\ parallel\ sides)* Height`

Area of trapezium =
`0.5* (100+140)* 80`

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:

`(1)/(2000)=(x)/(7000)\\\\2000x=7000\\\\x=(7000)/(2000)=3.5=3(1)/(2)`

Therefore, the number of bags of seeds required to cover 7000 square feet of lawn is three and a half.