A design is made on a rectangular tile of dimensions 50 cm x 17 cm as

1.	A design is made on a rectangular tile of dimensions 50 cm x 17 cm as shown in figure. The design shows 8 triangle, each of sides 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tiles.
Answer» For area of one triangle, a = 25, b = 17, c = 26 s = (a + b + c)/2 ⇒ s = (25 + 17 + 26)/2 = 68/2 = 34 Area(Δ) = √s(s-a)(s-b)(s-c) ⇒ Area(Δ) = √34(34-25)(34-17)(34-26) ⇒ Area(Δ) = √34×9×17×8 ⇒ Area(Δ) = 204 cm² Area of design = 8 × Area(Δ) ∴ Area of design = 8 × 204 = 1632 cm² Area of remaining tile = Area of rectangle – Area of design ⇒ Area of remaining tile = (50×70) – 1632 ⇒ Area of remaining tile = 3500 – 1632 = 1868 cm²

A design is made on a rectangular tile of dimensions 50 cm x 17 cm as shown in figure. The design shows 8 triangle, each of sides 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tiles.

Answer»

For area of one triangle,

a = 25, b = 17, c = 26

s = (a + b + c)/2

⇒ s = (25 + 17 + 26)/2 = 68/2 = 34

Area(Δ) = √s(s-a)(s-b)(s-c)

⇒ Area(Δ) = √34(34-25)(34-17)(34-26)

⇒ Area(Δ) = √34×9×17×8

⇒ Area(Δ) = 204 cm²

Area of design = 8 × Area(Δ)

∴ Area of design = 8 × 204 = 1632 cm²

Area of remaining tile = Area of rectangle – Area of design

⇒ Area of remaining tile = (50×70) – 1632

⇒ Area of remaining tile = 3500 – 1632 = 1868 cm²