The expression . 40 + 20π and 10 + 10 + 10π + 10 + 10 + 10π gives the correct value of the perimeter is 102.8 .
We have to determine, the perimeter of the given shape in the question.
According to the question,
The squares have a side length of 10 and 1 square side is the radius of the half-circles.
There are two half-circles,
To find the circumference for one full circle:
[tex]C = 2\pi r[/tex]
Where radius = 10
[tex]C = 2\times 3.14 \times 10\\\\C = 62.8[/tex]
The circumference of the circles is 62.8.
To find the perimeter of the exposed squares with side length 10.
There are 4 exposed sides, which equals one square.
Therefore, perimeter p is given as,
[tex]P = 10+10+10+10\\\\P = 40[/tex]
On adding the perimeter of the circle and the square together:
[tex]P = 62.8+ 40 = 102.8[/tex]
Check all the statement which give perimeter of the shape,
[tex]40+20\pi = 40+ 20\times3.14 = 102.8\\\\20\pi = 20 \times 3.14 = 62.8\\\\120+20\times \pi = 120+20\times3.14= 182.8\\\\300 + 100\times\pi = 300+100\times3.14 = 614\\ \\10+10+10\times\pi +10+10+10\times\pi = 40+ 20\times3.14 = 102.8[/tex]
Hence, The expression . 40 + 20π and 10 + 10 + 10π + 10 + 10 + 10π gives the correct value of the perimeter is 102.8 .
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