Anjali wants to renovate her hall room which is rectangular in shape with dimensions 6m x 5m. She decided to make the following changes.
• Change the square-shaped tiles to triangular-shaped tiles.
• A circle-shaped carpet in the center.
• Install floor wood molding around the entire room.
Q1. Are these tiles congruent?Which congruence condition they hold?Identify any two congruence shapes from your structure model.
Q2. Find the number of triangular tiles required for the entire room, if the base and height of each tile is 60cm and 50 cm respectively.
Q3. If a 2m diameter carpet is placed at the center of the hall, how much area is left uncarpeted?
Q4. Find the ratio of the area of your hall room in the making coding structure model to the area of Anjali’s hall room (Take the rectangular part from your structure)?
Answers
Given : hall room rectangular in shape with dimensions 6m x 5m.
base and height of each tile is 60cm and 50 cm respectively.
2m diameter carpet is placed at the center of the hall,
To Find : number of triangular tiles required for the entire room
how much area is left uncarpeted
ratio of area of a triangular tile to area of the carpet placed at the center of the hall.
Solution:
Triangular tiles are congruent using SSS congruence
base and height of each tile is 60cm and 50 cm respectively.
=> area of one tile = (1/2) * 60 * 50 = 1500 cm²
hall room rectangular in shape with dimensions 6m x 5m.
1 m = 100 cm
6 m = 600 cm
5 m = 500 cm
Hall Area = 600 x 500 = 300000 cm²
Number of tiles required = 300000 / 1500 = 200
2m diameter carpet is placed at the center of the hall,
Radius = 1 m = 100 cm
Area of circle = πr²
Area of carpet = 3.14 * 100² = 31400 cm²
= 3.14 m²
area is left uncarpeted = 300000 - 31400
= 2,68,600 cm²
= 26.68 m²
ratio of area of a triangular tile to area of the carpet placed at the center of the hall.
= 30 : 3.14
= 3000 : 314
= 1500 : 157
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