Have we have two legs the same length then this is what is called and Isosceles Triangle.
So this is like two Right Triangles back to back.
I assume they are called this as they have a right angle (90^o90o) in them.
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The area of a triangle is 1/2" base "xx" height"12 base × height
So we need the height. We use Pythagoras to determine this:
color(blue)("Determine the height")Determine the height
Let the height be hh
Note that 7.6/2-> 3.87.62→3.8
h^2+(3.8)^2=5^2h2+(3.8)2=52
Subtract (3.8)^2(3.8)2 from both sides
h^2=5^2-(3.8)^2h2=52−(3.8)2
square root both sides
h=sqrt(5^2-(3.8)^2) h=√52−(3.8)2
h=sqrt(10.56)h=√10.56 this give a a very long decimal so switching to fractions to retain precision:
Note that 3.8 = 38/103.8=3810 and that 5^2=25=2500/10052=25=2500100
h=sqrt(5^2-(38/10)^2) h=√52−(3810)2
h=sqrt(2500/100-1444/100)h=√2500100−1444100
h=sqrt( 1056/100) =sqrt(1056)/sqrt(100) = sqrt(1056)/10h=√1056100=√1056√100=√105610
If you are ever not sure about roots do a quick sketch of a prime number factor tree:
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From this we have sqrt(1056)=sqrt(2^2xx2^2xx2xx3xx11) = 4sqrt(66)√1056=√22×22×2×3×11=4√66
Thus h=(4sqrt(66))/10 = (2sqrt(66))/5h=4√6610=2√665
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color(blue)("Determine the area")Determine the area
"area "= 1/2xx" base"xx" height"area =12× base× height
"area "= 1/cancel(2)xx7.6xx(cancel(2)sqrt(66))/5
"area "= 1.52sqrt(66)color(white)("d") as an exact value.
"area "~~ 12.348color(white)("d") to 3 decimal places
