Find the area of a trapezoid when [tex]$b_1 = 3$ cm[/tex], [tex][tex]$b_2 = 4$[/tex] cm[/tex], and [tex]$h = 8$ cm[/tex].

[tex]\text{Area} = \square \text{ square centimeters}[/tex]



Answer :

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.