Question

PLEASE HELP IM SO CONFUSED WITH THIS!!!!

Answer 1

`(91)/(400)`

Explanation:

Given:

A square (all sides are equal)

AC = 20 (diagonal)

PI = 7

First, we can find the side length of the whole square:

`d(diagonal) = a √(2)`

`a √(2) = 20`

Divide both sides of the equation by √2 to make a the subject:

`a = (20)/( √(2) ) = (20 √(2) )/(2) = 10 √(2)`

Now, let's do the same thing, but with the smaller square on the top right:

`pr √(2) = 7`

`pr = ri = (7)/( √(2) ) = (7 √(2) )/(2) = 3.5 √(2)`

`ic = 10 √(2) - 3.5 √(2) = 6.5 √(2)`

We also have to find the areas of the shaded rectangles and the whole square:

`a(shaded) = 6. 5√(2) * 3.5 √(2) = 45.5`

`a(square) = ({10 √(2)) }^(2) = 200`

Let's call the event A:

A - "The dart hits the shaded region"

All outcomes:

n = 200 (since it can randomly hit the whole area)

Favorable outcomes:

m (A) = 45,5 (since it only need to hit the shaded region)

`p(a) = (m(a))/(n) = (45.5)/(200) = (91)/(400)`