क्षेत्रफल

कुनै तल (समतल वा वक्रतल)का द्वि-बीमीय (द्वि-आयामी) आकारका परिमाण (माप)लाई क्षेत्रफल भन्दछन्। जस क्षेत्रका क्षेत्रफलको कुरा गरिन्छ त्यो क्षेत्र प्रायः कुनै बन्द वक्र (closed curve)देखि घिरा हुन्छ। यसलाई प्राय: m^२ (वर्ग मीटर)मा मापिन्छ।

क्षेत्रफलको एकाई

क्षेत्रफलका मापनका लागि प्रयुक्त केही प्रमुख एकाई यस प्रकार छन्:

मेट्रिक

वर्ग मीटर (मी² वा m²) = SI व्युत्पन्न एकाई

एयर (are) (a) = १०० वर्ग मीटर

हेक्टेयर (hectare वा ha) = १०,००० वर्ग मी

वर्ग किलोमीटर ( किमी² वा km²) = १,०००,००० वर्ग मी

वर्ग फुट (square foot) = १४४ वर्ग इन्च (square inches) = ०.०९२९०३०४ वर्ग मी

वर्ग गज (square yard) = ९ वर्ग फीट = ०.८३६१२७३६ वर्ग मीटर

वर्ग मील (square mile) = ६४० एकड (acres) = २.५८९९८८११०३ वर्ग किमी (km²)

विभिन्न आकृतिहरूका क्षेत्रफलका सूत्र

केही समतल आकृतीहरू

क्षेत्रफलका प्रमुख समीकरण:

आकृति	समीकरण	चरहरूको अर्थ (meaning of variables)
वर्ग (square)	${\displaystyle s^{2}\,\!}$	${\displaystyle s}$ वर्गका भुजाको लम्बाई हो।
त्रिभुज (triangle)	${\displaystyle {\frac {\sqrt {3}}{4}}s^{2}\,\!}$	${\displaystyle s}$ त्रिभुजका भुजाको लम्बाई हो।
सम षट्भुज (Regular hexagon)	${\displaystyle {\frac {3{\sqrt {3}}}{2}}s^{2}\,\!}$	${\displaystyle s}$ is the length of one side of the hexagon.
सम अष्टभुज (Regular octagon)	${\displaystyle 2(1+{\sqrt {2}})s^{2}\,\!}$	${\displaystyle s}$ is the length of one side of the octagon.
कुनै पनि सम बहुभुज (regular polygon)	${\displaystyle {\frac {1}{2}}ap\,\!}$	${\displaystyle a}$ is the apothem, or the radius of an inscribed circle in the polygon, and ${\displaystyle p}$ is the perimeter of the polygon.
कुनै पनि सम बहुभुज (२)	${\displaystyle {\frac {P^{2}/n}{4\cdot \tan(\pi /n)}}\,\!}$	${\displaystyle P}$ is the Perimeter and ${\displaystyle n}$ is the number of sides.
कुनै पनि सम बहुभुज (३)	${\displaystyle {\frac {P^{2}/n}{4\cdot \tan(180^{\circ }/n)}}\,\!}$	${\displaystyle P}$ is the Perimeter and ${\displaystyle n}$ is the number of sides.
आयत (Rectangle)	${\displaystyle lw\,\!}$	${\displaystyle l}$ and ${\displaystyle w}$ are the lengths of the rectangle's sides (length and width).
समान्तर चतुर्भुज (Parallelogram)	${\displaystyle bh\,\!}$	${\displaystyle b}$ and ${\displaystyle h}$ are the length of the base and the length of the perpendicular height, respectively.
सम चतुर्भुज (Rhombus)	${\displaystyle {\frac {1}{2}}ab}$	${\displaystyle a}$ and ${\displaystyle b}$ are the lengths of the two diagonals of the rhombus.
त्रिभुज (२)	${\displaystyle {\frac {1}{2}}bh\,\!}$	${\displaystyle b}$ and ${\displaystyle h}$ are the base and altitude (measured perpendicular to the base), respectively.
त्रिभुज (३)	${\displaystyle {\frac {1}{2}}ab\sin C\,\!}$	${\displaystyle a}$ and ${\displaystyle b}$ are any two sides, and ${\displaystyle C}$ is the angle between them.
वृत्त (Circle)	${\displaystyle \pi r^{2},\,\!}$ or ${\displaystyle \pi d^{2}/4\,\!}$	${\displaystyle r}$ is the radius and ${\displaystyle d}$ the diameter.
दीर्घ वृत्त (Ellipse)	${\displaystyle \pi ab\,\!}$	${\displaystyle a}$ and ${\displaystyle b}$ are the semi-major and semi-minor axes, respectively.
समलम्ब चतुर्भुज (Trapezoid)	${\displaystyle {\frac {1}{2}}(a+b)h\,\!}$	${\displaystyle a}$ and ${\displaystyle b}$ are the parallel sides and ${\displaystyle h}$ the distance (height) between the parallels.
बेलनको सम्पूर्ण पृष्ट (Total surface area of a Cylinder)	${\displaystyle 2\pi r^{2}+2\pi rh\,\!}$	${\displaystyle r}$ and ${\displaystyle h}$ are the radius and height, respectively.
बेलनको पार्श्व पृष्ट (Lateral surface)	${\displaystyle 2\pi rh\,\!}$	${\displaystyle r}$ and ${\displaystyle h}$ are the radius and height, respectively.
शंकुको सम्पूर्ण पृष्ट (Total surface area of a Cone)	${\displaystyle \pi r(l+r)\,\!}$	${\displaystyle r}$ and ${\displaystyle l}$ are the radius and slant height, respectively.
शंकुको पार्श्व पृष्ट वा वक्र पृष्ठ	${\displaystyle \pi rl\,\!}$	${\displaystyle r}$ and ${\displaystyle l}$ are the radius and slant height, respectively.
गोलो (sphere)को सम्पूर्ण पृष्ठ	${\displaystyle 4\pi r^{2}\,\!}$ or ${\displaystyle \pi d^{2}\,\!}$	${\displaystyle r}$ and ${\displaystyle d}$ are the radius and diameter, respectively.
दीर्घ वृत्ताभको सम्पूर्ण पृष्ठ (Total surface area of an ellipsoid)		See the article.
वृत्तीय क्षेत्र (Circular sector)	${\displaystyle {\frac {1}{2}}r^{2}\theta \,\!}$	${\displaystyle r}$ and ${\displaystyle \theta }$ are the radius and angle (in radians), respectively.
x-अक्षका परितः f(x)लाई घुमाउनमा बनेका पृष्ठको क्षेत्रफल	${\displaystyle 2\pi \int _{a}^{b}|f(x)|{\sqrt {1+(f'(x))^{2}}}dx}$
f(x)लाई y-अक्षका परितः घुमाउनाले बनेका तलको क्षेत्रफल	${\displaystyle 2\pi \int _{a}^{b}|x|{\sqrt {1+(f'(x))^{2}}}dx}$ -->

विसम बहुभुजहरू (irregular polygons)को क्षेत्रफल सर्वेयरका सूत्रद्वारा निकाल्न सकिन्छ।^[1]

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