Question

CASEY HAS A BACKYARD THAT IS A 50-BY-50 FOOT SQUARE. SHE TURNED OVER AN IRREGULARLY-SHAPED PLOT OF SOIL TO PLAN A GARDEN. TO FIND THE AREA OF THE GARDEN, 1,500 RANDOM POINTS ARE GENERATED AND 420 OF THE POINTS LAND INSIDE THE IRREGULARLY-SHAPED GARDEN. WHAT IS THE AREA OF THE GARDEN?

Answer 1

Given the description of the irregular garden, the area will be given by:
Area=(regular points)+1/2(irregular points)
regular points=1500
irregular points=420
thus
Area=1500+1/2(420)
Area=1500+210
Area=1710 ft²

Answer 2

Area of the garden is 700 square feet.

Explanation:

It is given that casey has backyard that is a 50 by 50 foot square. Area of yard is the product of its dimensions. So, the area of yard is

`A=50* 50=2500`

Let the area of the garden be x.

It is given that 420 out of 1500 points land inside the irregularly shaped garden. It means the proportion of these points is equal to the proportion of area.

`(420)/(1500)=(x)/(2500)`

`(420)/(1500)* 2500=x`

`700=x`

The value of x is 700. Therefore the area of the garden is 700 square feet.