![AM28](/avatars/41415.jpg)
AM28
03.08.2019 •
Mathematics
The markets on the path are spaced 200 meters apart. what is the distance in meters between points a and b?
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Ответ:
Area of the shaded region = 16(π - 2) in²
Perimeter of the shaded region = 4(π +
) in
Step-by-step explanation:
Since, BDC is a quarter of the circle with radius = 8 in.
Area of the quarter of the circle =![\frac{1}{4}(\pi)(r)^2](/tpl/images/1042/1387/3d09e.png)
=![\frac{1}{4}(64)\pi](/tpl/images/1042/1387/63b49.png)
= 16π in²
Area of ΔBCD =![\frac{1}{2}(\text{Base})(\text{Height})](/tpl/images/1042/1387/7363f.png)
=![\frac{1}{2}(8)(8)](/tpl/images/1042/1387/abee1.png)
= 32 in²
Since, area of the shaded part = Area of quarter of the circle - Area of triangle BCD
= (16π - 32)
= 16(π - 2) in²
Therefore, area of the shade region = 16(π - 2) in²
Similarly, length of arc BD =![\frac{1}{4}(2\pi r)](/tpl/images/1042/1387/a464d.png)
=![\frac{8\pi }{2}](/tpl/images/1042/1387/c54bc.png)
= 4π in.
Length of the diagonal of a square = (Side)√2
= 8√2 in
Perimeter of the shaded region = Length of arc BD + Length of diagonal BD
= 4π + 8√2
= 4(π + 2√2) in.