# kshetrafal

kisi tal (samatal ya vakratal) ke dvi-beemeeya (dvi-aayaami) aakaar ke parimaan (maap) ko kshetrafal kehte hain. jis kshetr ke kshetrafal ki baat ki jaati hai vah kshetr praay: kisi band vakr (closed curve) se ghira hota hai. ise praaya: m2 (varg meter) mein maapa jaata hai.

## kshetrafal ki ikaaiyaaain

kshetrafal ke maapan ke liye prayukt kuchh pramukh ikaaiyaaain is prakaar hain:

metrik
varg meter (mee² ya m²) = SI vyutpann ikaaiyaaain
air (are) (a) = 100 varg meter
hekteyar (hectare ya ha) = 10,000 varg mi
varg kilometer (kimee² ya km²) = 1,000,000 varg mi
varg foot (square foot) = 144 varg inch (square inches) = 0.09290304 varg mi
varg gaj (square yard) = 9 varg feet = 0.83612736 varg meter
varg meal (square mile) = 640 ekad (acres) = 2.5899881103 varg kimi (km²)

## vibhinn aakrutiyon ke kshetrafal ke sootr

kshetrafal ke pramukh sameekaran:
aakruti sameekaran charon ka arth (meaning of variables)
varg (square) $s^{2}\,\!$ $s$ varg ke bhuja ki lambaai hai.
tribhuj (triangle) ${\frac {\sqrt {3}}{4}}s^{2}\,\!$ $s$ is the length of one side of the triangle.
sam shatbhuj (Regular hexagon) ${\frac {3{\sqrt {3}}}{2}}s^{2}\,\!$ $s$ is the length of one side of the hexagon.
sam ashtabhuj (Regular octagon) $2(1+{\sqrt {2}})s^{2}\,\!$ $s$ is the length of one side of the octagon.
koi bhi sam bahubhuj (regular polygon) ${\frac {1}{2}}ap\,\!$ $a$ is the apothem, or the radius of an inscribed circle in the polygon, and $p$ is the perimeter of the polygon.
koi bhi sam bahubhuj (2) ${\frac {P^{2}/n}{4\cdot \tan(\pi /n)}}\,\!$ $P$ is the Perimeter and $n$ is the number of sides.
koi bhi sam bahubhuj (3) ${\frac {P^{2}/n}{4\cdot \tan(180^{\circ }/n)}}\,\!$ $P$ is the Perimeter and $n$ is the number of sides.
aayat (Rectangle) $lw\,\!$ $l$ and $w$ are the lengths of the rectangle's sides (length and width).
samaantar chaturbhuj (Parallelogram) $bh\,\!$ $b$ and $h$ are the length of the base and the length of the perpendicular height, respectively.
sam chaturbhuj (Rhombus) ${\frac {1}{2}}ab$ $a$ and $b$ are the lengths of the two diagonals of the rhombus.
tribhuj (TRIANGLE) ${\frac {1}{2}}bh\,\!$ $b$ and $h$ are the base and altitude (measured perpendicular to the base), respectively.
tribhuj (3) ${\frac {1}{2}}ab\sin C\,\!$ $a$ and $b$ are any two sides, and $C$ is the angle between them.
vrutt (Circle) $\pi r^{2},\,\!$ or $\pi d^{2}/4\,\!$ $r$ is the radius and $d$ the diameter.
deergh vrutt (Ellipse) $\pi ab\,\!$ $a$ and $b$ are the semi-major and semi-minor axes, respectively.
samalamb chaturbhuj (Trapezoid) ${\frac {1}{2}}(a+b)h\,\!$ $a$ and $b$ are the parallel sides and $h$ the distance (height) between the parallels.
belan ka sampoorn prusht (Total surface area of a Cylinder) $2\pi r^{2}+2\pi rh\,\!$ $r$ and $h$ are the radius and height, respectively.
belan ka paarshv prusht (Lateral surface) $2\pi rh\,\!$ $r$ and $h$ are the radius and height, respectively.
shanku ka sampoorn prusht (Total surface area of a Cone) $\pi r(l+r)\,\!$ $r$ and $l$ are the radius and slant height, respectively.
shanku ka paarshv prusht ya vakr prushth $\pi rl\,\!$ $r$ and $l$ are the radius and slant height, respectively.
gole (sphere) ka sampoorn prushth $4\pi r^{2}\,\!$ or $\pi d^{2}\,\!$ $r$ and $d$ are the radius and diameter, respectively.
deergh vruttaabh ka sampoorn prushth (Total surface area of an ellipsoid) See the article.
vrutteeya kshetr (Circular sector) ${\frac {1}{2}}r^{2}\theta \,\!$ $r$ and $\theta$ are the radius and angle (in radians), respectively.
x-aksh ke parit: f(x) ko ghumaane par bane prushth ka kshetrafal $2\pi \int _{a}^{b}|f(x)|{\sqrt {1+(f'(x))^{2}}}dx$ f(x) ko y-aksh ke parit: ghumaane se bane tal ka kshetrafal $2\pi \int _{a}^{b}|x|{\sqrt {1+(f'(x))^{2}}}dx$ -->

vism bahubhujon (irregular polygons) ka kshetrafal sarveyar ke sootr se nikaala ja sakta hai.