To find the area of a trapezoid, we'll use the formula for the area, which is:
[tex]\[ A = \frac{1}{2} \left( b_1 + b_2 \right) h \][/tex]
Here are the given values:
- The length of the first base, [tex]\( b_1 \)[/tex], is [tex]\( 3.6 \)[/tex] cm.
- The length of the second base, [tex]\( b_2 \)[/tex], is [tex]\( 12 \frac{1}{3} \)[/tex] cm.
- The height, [tex]\( h \)[/tex], is [tex]\( \sqrt{5} \)[/tex] cm.
### Step-by-Step Solution:
1. Convert the mixed number to an improper fraction:
[tex]\[ 12 \frac{1}{3} \,, \text{ can be written as } 12 + \frac{1}{3} \][/tex]
2. Convert to decimal:
[tex]\[ 12 + \frac{1}{3} = 12.333333333333334 \, .\][/tex]
Now we have:
- [tex]\( b_1 = 3.6 \)[/tex] cm
- [tex]\( b_2 = 12.333333333333334 \)[/tex] cm
- [tex]\( h = \sqrt{5} \approx 2.23606797749979 \)[/tex] cm
3. Sum of the bases:
[tex]\[ b_1 + b_2 = 3.6 + 12.333333333333334 = 15.933333333333334 \][/tex] cm
4. Multiply by height:
[tex]\[ \left( b_1 + b_2 \right) h = 15.933333333333334 \times 2.23606797749979 \][/tex]
5. Divide by 2:
[tex]\[ A = \frac{1}{2} \left( 15.933333333333334 \times 2.23606797749979 \right) \][/tex]
[tex]\[ A = \frac{1}{2} \times 35.628016441496654 \][/tex]
[tex]\[ A = 17.814008220748327 \][/tex]
### Result:
The area of the trapezoid is approximately [tex]\( 17.814 \, \text{cm}^2 \)[/tex].
