MHB Finding the Area of Shaded Part

  • Thread starter Thread starter karush
  • Start date Start date
  • Tags Tags
    Area
AI Thread Summary
The discussion focuses on calculating the area of a shaded region involving triangles and a sector of a circle. The area of triangle OAPB is derived from the areas of similar triangles OAP and OBP, resulting in a total of 110.4 cm². The area of the sector is calculated as 94.2 cm², leading to a shaded area of 16.2 cm² after subtraction. An alternative method for finding the shaded area is also presented, yielding approximately 15.33 cm². The calculations have been verified through multiple approaches, confirming their accuracy.
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
find the area of the shaded part

first I tried to find out the area of $OAPB$ which can be found by adding triangles $OAP$ and $OBP$ which are similar, $AP$ and $BP$ are perpendicular to the radius and tangent to the circle$BP = 12\tan{37.5^0}=9.2 cm^2$

area $\Delta OBP= \frac{1}{2}(12)(9.2)=52.2 cm^2$

area $OAPD = 2(52.2)= 110.4 cm^2$

area of sector $\frac{75}{360}\pi 12^2 = 94.2 cm^2$

so shaded area $= 110.4 - 92.2 = 16.2 cm^2$

just seeing if this is OK i went over it quite a few times...
no ans given ...(Cool)(Coffee)
 
Mathematics news on Phys.org
Area of $\displaystyle OAPB$ is:

$\displaystyle 15\cdot12\sin(37.5^{\circ})$

Subtract the area of sector $\displaystyle OAB$:

$\displaystyle A_S=15\cdot12\sin(37.5^{\circ})-\frac{1}{2}12^2\cdot\frac{5\pi}{12}=180\sin(37.5^{\circ})-30\pi\approx15.329277613875924$

I have verified this using another method as well.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top