Find the area of a regular octagon ABCDEFGH as shown in the following figure, where
FQ=8m,GD=22m,PB=8m,CD=10m . pls see the attachment and solve quickly and step by step
FQ=8m,GD=22m,PB=8m,CD=10m . pls see the attachment and solve quickly and step by step
Answers & Comments
Step-by-step explanation:
Let the line segment be AB, then as given AB cos α = 3, AB cos β = 4, AB cos γ = 5
⇒ AB2 (cos2α + cos2β + cos2γ) = 32 + 42 + 52
AB = √[9 + 16 + 25] = 5√2,
Verified answer
Area of Trapezium FEDG = 1/2 x Height (FQ) x (sum of parallel sides FE+GD)
= 1/2 x 8 x (22+10)
= 4 x 32
=128m square
Area of Rectangle GDCH = Length(GD) x Breadth(CD)
= 22 x 10
=220m square
Area of Trapezium HCBA = 1/2 x Height (PB) x (sum of parallel sides AB+CH)
= 1/2 x 8 x (22+10)
= 4 x 32
=128m square
Area of Octagon = Area of Trapezium FEDG + Area of Rectangle GDCH + Area of Trapezium HCBA = 128 + 220 + 128 = 476m square