# 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.

2
by priyankasharma

2015-10-21T15:18:20+05:30

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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

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...