Answer:
Area of the shaded region = 23.33 in²
Step-by-step explanation:
Area of a sector = 
Where θ = Central angle subtended by an arc
r = radius of the circle
Area of the sector BCD = 
= 52.36 in²
Area of equilateral triangle BCD = 
= 
=
in²
= 43.30 in²
Area of the shaded portion in ΔBCD = 52.36 - 43.3
= 9.06 in²
Area of sector CAD = 
= 39.27 in²
Area of right triangle CAD = 
= 
=
= 25 in²
Area of the shaded part in the ΔACD = 39.27 - 25
= 14.27 in²
Area of the shaded part of the figure = 9.06 + 14.27
= 23.33 in²
Answer:
56
Step-by-step explanation:
from theorem , VR/SR=VU/UT
Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:

Where <em>w</em> is the width and <em>l</em> is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>
![\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdA%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5Bw%5Cell%5D)
By the Product Rule:

Since we know that dl/dt = 6 and that dw/dt = 5:

We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:

The area of the rectangle is increasing at a rate of 84 square centimeters per second.
It is less than 2. I hope this helps!