Video Transcript
The two triangles in the given
figure are congruent. Work out the area of triangle
๐ด๐ต๐ถ.
Weโre told here that the two
triangles are congruent. That means that pairs of
corresponding angles will be equal and pairs of corresponding sides will be
equal. Weโll need to use this fact to help
us work out the area of triangle ๐ด๐ต๐ถ.
We can recall that to find the area
of a triangle, we multiply half times the base times the perpendicular height. When we look at triangle ๐ด๐ต๐ถ, we
can see that we donโt know the base length of this triangle, which is why weโll need
to use the fact that this is congruent with triangle ๐ท๐ธ๐น to help us work out the
length of ๐ต๐ถ.
In this question, we werenโt given
a congruency relationship, so weโll need to establish which sides correspond to
which sides. Letโs start with the hypotenuse,
the longest side on triangle ๐ด๐ต๐ถ. This will correspond with the
longest side or hypotenuse on our other triangle. So, ๐ด๐ถ and ๐ท๐น will be
congruent.
On triangle ๐ด๐ต๐ถ, if we go from
the hypotenuse down to the right angle along the line ๐ด๐ต, this corresponds to the
same journey or path from the hypotenuse down to the right angle on triangle
๐ท๐ธ๐น. So, ๐ด๐ต and ๐ท๐ธ will be the same
length of 5.1. The final pair of sides ๐ต๐ถ and
๐ธ๐น will also be congruent, and theyโll be of length 4.1.
We now have enough information to
work out the area of triangle ๐ด๐ต๐ถ. Filling in the values for our base
length of 4.1 and the perpendicular height of 5.1, weโll have a half times 4.1 times
5.1. We can work out 4.1 times 5.1 by
calculating 41 times 51. As our values had a total of two
decimal digits, then our answer will also have two decimal digits. Half of 20.91 will give us
10.455. The units here would be square
units. This is our answer for the area of
triangle ๐ด๐ต๐ถ. Note that if we worked out the area
of triangle ๐ท๐ธ๐น instead, we wouldโve got the same answer as both of these
triangles are congruent.
