What is the area of a triangle base=2 height =4, but its NOT a right triangle?

1 Answer
Alan P.
Jul 23, 2015

Area of a triangle is #1/2 xx base xx height#
(there is no requirement that the triangle be a right triangle for this formula)
The given triangle has an area of 4

Explanation:

Only continue if you don't understand why
#color(white)("XXXX")##"Area"_"triangle" = 1/2xx"base"xx"height"#

Consider the two triangles below:
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For the Acute Angled Triangle ABC
#triangle ABC# is composed of #triangle ADC# and #triangle DBC#

#triangle ADC = 1/2 square ADCP#
#triangle DBC = 1/2 square DBRC#

#triangle ABC#
#color(white)("XXXX")##= 1/2 (square ADCP + square DBRC)#

#color(white)("XXXX")##= 1/2 (square ABRP)#

and since the Area of #square ABRP = "base"xx"height"#

#color(white)("XXXX")#Area of #triangle ABC = 1/2 xx "base" xx "height"#

For the Obtuse Angled Triangle ABC
following a similar argument:
#triangle ADC = 1/2(square ADCP) = 1/2 ("base" + x) xx "height"#

#triangle BDC = 1/2(square BDCR) = 1/2 x xx "height"#

#triangle ABC = triangle ADC - triangle BDC#

Area of #triangle ABC#
#color(white)("XXXX")##= [ 1/2("base"+x)xx "height"] - [1/2[x xx "height"]#

#color(white)("XXXX")##= 1/2 "base" xx "height"#

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