#1**+2 **

The width is no problem.....it is just 4 times the radius of each circle = 4r = 4(2mm) = 8mm (1)

Note that joining the 3 radii will form an equilateral triangle with sides = 2r = 2 * 2mm = 4mm

The height of this triangle, h, can be found as

tan 60 = h/2

sqrt (3) = h / 2

2sqrt(3) = h

So....the height of the rectangle = [ 2sqrt(3) + 2r ] mm = [ 2sqt(3) + 2(2)] mm = [ 2qrt(3) + 4 ] mm (2)

So....the area of the rectangle = (1) * (2) =

[ 8 ] * [ 2sqrt (3) + 4 ] mm^2 =

[ 16sqrt (3) + 32 ] mm ^2

CPhill Feb 13, 2019

#3**+1 **

OK....

Note that 3sqrt (2) = = sqrt (9 * 2) = sqrt (18)

And 2sqrt (5) = sqrt (4 * 5) = sqrt (20)

So....we can find the height o the triangle by the Pythagorean Theorem...

h ^2 = [ sqrt (20) ] ^2 - [sqrt (18) ] ^2

h^2 = 20 - 18

h^2 = 2

h = sqrt (2)

And the base = 3sqrt (2) + sqrt (2) = 4sqrt (2)

So....the area = (1/2)base * height = (1/2) [ 4 sqrt (2) ] [ sqrt (2) ] = (1/2) (4) [sqrt (2) ]^2 =

(1/2) (4) (2) =

4 cm ^2

CPhill Feb 13, 2019