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 side 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tile.
Solution:
Given, a design is made on a rectangular tile of dimension 50 cm × 70 cm
The design shows 8 triangles with dimensions 26 cm, 17 cm and 25 cm.
We have to find the total area of the design and the remaining area of the tile.
Area of rectangle = length × breadth
Area of rectangular tile = 50 × 70
= 3500 cm²
Consider one triangle out of 8 triangles,
By Heron’s formula,
Area of triangle = √s(s - a)(s - b)(s - c)
Where s = semiperimeter
s = (a + b + c)/2
Here, a = 26 cm, b = 17 cm and c = 25 cm
So, s = (26 + 17 + 25)/2
= 68/2
s = 34 cm
Area = √34(34 - 26)(34 - 17)(34 - 25)
= √34(8)(17)(9)
= √17 × 2 × 2 × 4 × 17 × 9
= 17 × 2 × 2 × 3
Area of one triangle = 204 cm²
Area of 8 triangles = 8(204) = 1632 cm²
Therefore, total area of the design is 1632 cm²
Remaining area of the tile = area of rectangular tile - area of 8 triangles
= 3500 - 1632
= 1868 cm²
Therefore, the remaining area of the tiles is 1868 cm²
✦ Try This: The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of a triangle.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12
NCERT Exemplar Class 9 Maths Exercise 12.4 Problem 8
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 side 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tile.
Summary:
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 side 26 cm, 17 cm and 25 cm. The total area of the design and the remaining area of the tile are 1632 cm² and 1868 cm²
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