Find the area of figure formed by a square of side 8cm and an isosceles triangle with bases one side of the square and perimeter as 18.
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the isosceles triangle has perimeter = 18
base = 8 cm
so the equal sides = (18 - 8) /2 = 5
altitude and area are shown in the diagram... total area = 76
area of the isosceles triangle can be also found using the formula of Heron:
Δ = √[s (s-a) (s-b)(s-c)
here a = 8, b = 5 c = 5 so s = (8+5+5)/2 = 9
Δ = area = √[ 9*1*4*4] = 12 sq cm
Add this to the area of square = 8 * 8 = 64 cm²
total 76 cm²
base = 8 cm
so the equal sides = (18 - 8) /2 = 5
altitude and area are shown in the diagram... total area = 76
area of the isosceles triangle can be also found using the formula of Heron:
Δ = √[s (s-a) (s-b)(s-c)
here a = 8, b = 5 c = 5 so s = (8+5+5)/2 = 9
Δ = area = √[ 9*1*4*4] = 12 sq cm
Add this to the area of square = 8 * 8 = 64 cm²
total 76 cm²
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priyankasharma:
i am your big fan sir thanks a lot
but sir we have no altitude. so how i get area
use the formula for area of isosceles triangle ABC: one way is to find altitude using the Pythagoras theorem. so draw a perpendicular from B on to AC..
otherwise use the formula for area of triangle with 3 sides given...
answer is modified.
Answered by
19
area of the square= 8x8 = 64sq.cm
area of triangle= (1/2) base x height
base=8cm.
Since the triangle is isosceles, the other 2 sides would be equal measuring 5cm each.
Height could be found using Pythogoras theorem[5^2- 4^2=3^2], we get height=3cm.
Area of triangle=(1/2)(3)(8)=12sq.cm
64+12=76 sq.cm
area of triangle= (1/2) base x height
base=8cm.
Since the triangle is isosceles, the other 2 sides would be equal measuring 5cm each.
Height could be found using Pythogoras theorem[5^2- 4^2=3^2], we get height=3cm.
Area of triangle=(1/2)(3)(8)=12sq.cm
64+12=76 sq.cm
4 is come from where
draw an imaginary perpendicular opposite to the side measuring 8cms. This would cut the triangle into half forming 2 right angled triangles. Apply Pythogoras theorem to one half and you will get the height of perpendicular which is height of the triangle. I hope this helps.
use Heron's formula..
Yes Sir, even that can be used.
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