Lesson Formulas for area of a triangle
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<H2>Formulas for area of a triangle</H2> 1. {{{S}}} = {{{a*h/2}}}. The area of a triangle equals half the product of the measure of any its side ({{{a}}}) and the measure of the altitude drawn to this side ({{{h}}}). 2. {{{S}}} = {{{a*b*sin(gamma)/2}}}. The area of a triangle equals half the product of the measures of any two its sides ({{{a}}} and {{{b}}}) and the sines of the angle included by these sides. 3. {{{S}}} = {{{r*p}}}. The area of a triangle equals the product of its semi-perimeter {{{p}}} and the radius of the inscribed circle {{{r}}}. 4. {{{S}}} = {{{sqrt(p(p-a)(p-b)(p-c))}}} = {{{sqrt(((a+b+c)/2)*((a+b-c)/2)*((a-b+c)/2)*((b+c-a)/2))}}}. It is the Heron's formula named after the ancient Greek mathematician Heron. Here {{{a}}}, {{{b}}} and {{{c}}} are the measures of a triangle sides and {{{p}}} is half the perimeter: {{{p}}} = {{{(a + b + c)/2}}}. 5. {{{S}}} = {{{abc/4R}}}. Here {{{a}}}, {{{b}}} and {{{c}}} are the measures of a triangle sides and {{{R}}} is the radius of the circumscribed circle. <H3>Right-angled triangle</H3> 6. {{{S}}} = {{{a*b/2}}}. The area of a right-angled triangle equals half the product of the measures of its legs {{{a}}} and {{{b}}}. <H3>Equilateral (or regular) triangle</H3> 7. {{{S}}} = {{{a^2*sqrt(3)/4}}}. The area of a regular triangle equals the square of its side {{{a}}} multiplied by {{{sqrt(3)/4}}} . My other lessons on the topic <B>Area</B> in this site are - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/What-is-area.lesson>WHAT IS area?</A> - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/-Proof-of-the-Heron%27s-formula-for-the-area-of-a-triangle.lesson>Proof of the Heron's formula for the area of a triangle</A> - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/One-more-proof-of-the-Heron%27s-formula-for-the-area-of-a-triangle.lesson>One more proof of the Heron's formula for the area of a triangle</A> - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Proof-of-the-formula-for-the-area-of-a-triangle-via-the-radius-of-the-inscribed-circle.lesson>Proof of the formula for the area of a triangle via the radius of the inscribed circle</A> - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Proof-of-the-formula-for-the-radius-of-the-circumscribed-circle.lesson>Proof of the formula for the radius of the circumscribed circle</A> - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Area-of-a-parallelogram.lesson>Area of a parallelogram</A> - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Area-of-a-trapezoid.lesson>Area of a trapezoid</A> - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Area-of-a-quadrilateral.lesson>Area of a quadrilateral</A> - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Area-of-a-sircumscribed-quadrilateral.lesson>Area of a quadrilateral circumscribed about a circle</A> and - <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Area-of-a-quadrilateral-inscribed-in-a-circle.lesson>Area of a quadrilateral inscribed in a circle</A> under the topic <B>Area and surface area</B> of the section <B>Geometry</B>, and - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-triangles.lesson>Solved problems on area of triangles</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-right-angled-triangles.lesson>Solved problems on area of right-angled triangles</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-regular-triangles.lesson>Solved problems on area of regular triangles</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-the-radius-of-inscribed-circles-and-semicircles.lesson>Solved problems on the radius of inscribed circles and semicircles</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-the-radius-of-a-circumscribed-circle.lesson>Solved problems on the radius of a circumscribed circle</A> - <A HREF=https://www.algebra.com/algebra/homework/word/geometry/A-Math-circle-level-problem-on-area-of-a-triangle.lesson>A Math circle level problem on area of a triangle</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-parallelograms.lesson>Solved problems on area of parallelograms</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-rhombis-rectangles-and-squares.lesson>Solved problems on area of rhombis, rectangles and squares</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-trapezoids.lesson>Solved problems on area of trapezoids</A> and - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-area-of-quadrilaterals.lesson>Solved problems on area of quadrilaterals</A> under the topic <B>Geometry</B> of the section <B>Word problems</B>. For navigation over the lessons on <B>Area of Triangles</B> use this file/link <A HREF=https://www.algebra.com/algebra/homework/Surface-area/REVIEW-OF-LESSONS-ON-AREA-OF-TRIANGLES.lesson>OVERVIEW of lessons on area of triangles</A>. To navigate over all topics/lessons of the Online Geometry Textbook use this file/link <A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A>.
