The area of the gate is 79.216 m²
How to determine area of composite figures.
The figure is a composite shade made up of a rectangle,a hollow trapezoid and two rectangles.
To find the area of the figure, we find the area of the individual components and sum them up.
Area of trianglular part
Area of triangle = 1/2 bxh
h = 6 m, b = 4.25 m
A = 1/2*4.25*6
= 12.75 m²
Area of hollow trapezoid = area of trapezoid - area of semicircular part.
A = 1/2(a+b)h - πr²/2
a = 4.25 m, b = 10 m, h = 17-(6+5) = 6 m,
r = d/2 = 4/2 = 2 m, π = 3.142
Substitute
A = 1/2(4.25 + 10)*6 - (3.142*2²/2)
= 42.75 - 6.284
= 36.466 m²
Area of rectangular parts
Area of rectangle = bxh
b = 3 m, h = 5 m
Area = 3*5
= 15 m² times 2 because there are two rectangles
= 30 m²
Area of the gate = 12.75 + 36.466 + 30
= 79.216 m²
Therefore the area of the gate is 79.216 m²