Question

What is the area of the composite figure? (6π 4) cm2 (6π 16) cm2 (12π 4) cm2 (12π 16) cm2

Answer 1

The area of the considered composite figure is given by: Option: 6π + 16 cm²

How to calculate the surface area of a composite figure?

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

Thus, we have:

$\text{Area of composite figure} = \sum (\text{Area of composing figures})$

That ∑ sign shows "sum"

For this case, the missing image is attached below.

As visible, the area of the figure = Sum of area of those 3 semi circles + Area of that square(its square because it has 4 equal sides in which adjacent sides are perpendicular) in between.

The side of the square is of 2+2=4 cm( as half of its side is 2 cm), thus, Area of that square = 4² = 16 cm²

All those 3 semicircles has radius = 2 cm

Since radius is same, so area of those 3 semicircle is same = $\dfrac{\pi r^2}{2} = \dfrac{\pi (2)^2}{2} = 2 \pi\: \rm cm^2$

Thus, we get:

Area of the composite figure = $2 \pi +2 \pi +2 \pi + 16 \: \rm cm^2 = 6 \pi+ 16 \: \rm cm^2$

Learn more about area of a composite figure here:

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