# 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

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

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