To find the area of a trapezoid, we use the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \][/tex]
where [tex]\( b_1 \)[/tex] and [tex]\( b_2 \)[/tex] are the lengths of the two parallel sides (bases) and [tex]\( h \)[/tex] is the height.
Given:
- [tex]\( b_1 = 3 \)[/tex] cm
- [tex]\( b_2 = 4 \)[/tex] cm
- [tex]\( h = 8 \)[/tex] cm
Substitute these values into the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times (3 \text{ cm} + 4 \text{ cm}) \times 8 \text{ cm} \][/tex]
First, add the lengths of the bases:
[tex]\[ b_1 + b_2 = 3 \text{ cm} + 4 \text{ cm} = 7 \text{ cm} \][/tex]
Next, multiply the sum of the bases by the height:
[tex]\[ 7 \text{ cm} \times 8 \text{ cm} = 56 \text{ cm}^2 \][/tex]
Finally, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \text{Area} = \frac{1}{2} \times 56 \text{ cm}^2 = 28 \text{ cm}^2 \][/tex]
So, the area of the trapezoid is [tex]\( 28 \)[/tex] square centimeters.
