Given: Lateral area = 68

AO = 3.4

Find: m∠SAB

Step-by-step explanation:

Surface Area of a Cone

The surface area of a cone is given by

Where r is the radius and hs is the slant height measured from the top to any point at the circumference of the base. The cone shown in the figure has a radius r=3.4 and a surface area of 68.

Solving for hs

But hs is equal to AS. The triangle SAO has an angle of 90° at the point O. The required angle  m∠SAB can be found by applying the cosine ratio:

Thus

45

step-by-step explanation:

30+15

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2