SOLUTION: Determine the perimeter and area: https://i.ibb.co/ZzVXsg2g/ED907482-977-D-4-DD4-9636-317-CA1-C38-D45.jpg

Algebra ->  Surface-area -> SOLUTION: Determine the perimeter and area: https://i.ibb.co/ZzVXsg2g/ED907482-977-D-4-DD4-9636-317-CA1-C38-D45.jpg      Log On


   



Question 1210338: Determine the perimeter and area:
https://i.ibb.co/ZzVXsg2g/ED907482-977-D-4-DD4-9636-317-CA1-C38-D45.jpg

Found 2 solutions by ikleyn, mccravyedwin:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Determine the perimeter and area:
https://i.ibb.co/ZzVXsg2g/ED907482-977-D-4-DD4-9636-317-CA1-C38-D45.jpg
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The perimeter is (5 + 5) + (6+6) + pi%2Ar = 10+%2B+12+%2B+3.14159265%2A%288%2F2%29 = 34.5663706 m.


The area is the sum of the areas of two right-angled triangles PLUS the area of the rectangle 
PLUS the area of the semi-circle of the radius 8/2 = 4 m


Right angled triangles are (3-4-5)-triangles. The area of each such triangle is (1/2)*3*4 = 3*2 = 6 m^2.


So, the area under the question is 

    2*6 + 6*8 + %281%2F2%29%2Api%2Ar%5E2 = 12+%2B+48+%2B+%281%2F2%29%2A3.14159265%2A4%5E2 = 85.1327412 m^2.

Solved, with explanations.

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This problem is  EXTREMELY  simple.

It is of the level  " take what you see in the picture,
and plug the numbers into the simple formula ".

Thinking is not required and is not assumed . . .



Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!



The triangle at the top has: 
Area=expr%281%2F2%29%28base%29%28height%29=expr%281%2F2%29%288%29%283%29=12m%C2%B2

Its two slanted sided contribute 2(5m) = 10m to the perimeter.

The rectangle in the middle has:
Area=%28base%29%28height%29=%288%29%286%29=48m%C2%B2

It's left and right sides contribute 2(6m) = 12m to the perimeter.

The semi-circle at the bottom has diameter 8m and therefor 4m radius:
area=expr%281%2F2%29%2A%28pi%2Ar%5E2%29=expr%281%2F2%29%28pi%2A4%5E2%29=8pi m2.

It contributes expr%281%2F2%29%2A%282%2Api%2Ar%29=pi%2A4=4pi m to the circumference.

Area+=+12%2B+48+%2B+8pi+=+60%2B8pi m2

Perimeter+=+10m%2B12m%2B4pi+=+22%2B4pi m.

Edwin