Question
Find the cost of tiling the floor of a trapezoidal hall whose parallel sides are 25 m and 20 m and the distance between them is 16 m at the rate of \( ₹ 40 \) per \( \mathrm{m}^{2} \).
Ask by Ryan Cross. in India
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The total cost of tiling the trapezoidal hall is ₹14,400.
Solution
To calculate the cost of tiling the trapezoidal hall, follow these steps:
### **1. Calculate the Area of the Trapezoidal Hall**
The formula for the area \( A \) of a trapezoid is:
\[
A = \frac{(a + b)}{2} \times h
\]
where:
- \( a \) and \( b \) are the lengths of the parallel sides.
- \( h \) is the height (the perpendicular distance between the parallel sides).
Given:
- \( a = 25 \) meters
- \( b = 20 \) meters
- \( h = 16 \) meters
Plugging in the values:
\[
A = \frac{(25 + 20)}{2} \times 16 = \frac{45}{2} \times 16 = 22.5 \times 16 = 360 \, \text{m}^2
\]
### **2. Calculate the Total Cost**
The cost of tiling is given as ₹40 per square meter.
\[
\text{Total Cost} = \text{Area} \times \text{Cost per } \mathrm{m}^2 = 360 \times 40 = ₹14,400
\]
### **Final Answer**
The total cost of tiling the floor is **₹14,400**.
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Simplify this solution Mind Expander
To find the cost of tiling the trapezoidal hall, we first need to calculate the area of the trapezoid using the formula: \[ \text{Area} = \frac{1}{2} \times (a + b) \times h \] where \( a = 25 \, \text{m} \), \( b = 20 \, \text{m} \), and \( h = 16 \, \text{m} \). Substituting the values: \[ \text{Area} = \frac{1}{2} \times (25 + 20) \times 16 = \frac{1}{2} \times 45 \times 16 = 360 \, \text{m}^2 \] Next, we calculate the cost of tiling by multiplying the area by the cost per square meter: \[ \text{Cost} = \text{Area} \times \text{Rate} = 360 \, \text{m}^2 \times 40 \, ₹/\text{m}^2 = 14400 \, ₹ \] Hence, the total cost of tiling the floor is \( ₹ 14,400 \).
