A design is made on a rectangular tile of dimensions 50 cm 70 cm as shown in Fig. 12.7. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm os cut out. Find the total area of the design in $c m^{2}$

Open in App

Solution

$T h e a r e a o f t h e r e c t a n g u l a r t i l e = l e n g t h \times w i d t h = 70 \times 50 = 3500 T h e d e s i g n c o m p r i s e s o f 8 c o n g r u e n t t r i a n g l e s w i t h s i d e s 17 c m, 25 c m & 26 c m . A c c o r d i n g t o H e r o n^{'} s f o r m u l a t h e a r e a (A) o f t r i a n g l e w i t h s i d e s a, b & c i s g i v e n a s A = \sqrt[2]{[s (s - a) (s - b) (s - c)]} w h e r e 2 s = (a + b + c) . H e r e a = 17, b = 25, c = 26, s = \frac{(17 + 25 + 26)}{2} = \frac{68}{2} = 34 A r e a o f e a c h t r i a n g l e = \sqrt[2]{[34 \times (34 - 17) (34 - 25) (34 - 26)]} = \sqrt[2]{(34 \times 17 \times 9 \times 8)} = \sqrt[2]{(2 \times 17 \times 17 \times 3 \times 3 \times 2 \times 2 \times 2)} = 2 \times 2 \times 3 \times 17 = 12 \times 17 = 204 S o, t h e a r e a o f t h e t o t a l d e s i g n = a r e a o f a l l 8 t r i a n g l e s = 8 \times 204 = 1632 A n d t h e r e m a i n i n g a r e a o f r e c t a n g u l a r t i l e = 3500 - 1632 = 1868$

Suggest Corrections

Similar questions

Q. A design is made on a rectangular tile of dimensions

50 c m \times 70 c m

as shown in the given figure. The design shows

8

triangles, each of sides

26 c m, 17 c m

and

25 c m

. Find the total area of the design and the remaining area of the tile.

Question 8
A design is made on a rectangular tile of dimensions 50 cm $\times$ 70 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.

Question 8
A design is made on a rectangular tile of dimensions 50 cm $\times$ 70 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.