To solve the problem of finding the area of each trapezoid, we will use the formula for the area of a trapezoid:
\[
A = \frac{1}{2} (b_1 + b_2) h
\]
where:
- \( b_1 \) and \( b_2 \) are the lengths of the two parallel bases,
- \( h \) is the height (the perpendicular distance between the bases).
Let's solve each trapezoid step by step.
---
1)
Dimensions:
- \( b_1 = 8 \) in
- \( b_2 = 4 \) in
- \( h = 6 \) in
Formula Application:
\[
A = \frac{1}{2} (b_1 + b_2) h = \frac{1}{2} (8 + 4) \cdot 6
\]
\[
A = \frac{1}{2} \cdot 12 \cdot 6 = 6 \cdot 6 = 36 \text{ in}^2
\]
Answer:
\[
\boxed{36}
\]
---
2)
Dimensions:
- \( b_1 = 9 \) ft
- \( b_2 = 6 \) ft
- \( h = 4 \) ft
Formula Application:
\[
A = \frac{1}{2} (b_1 + b_2) h = \frac{1}{2} (9 + 6) \cdot 4
\]
\[
A = \frac{1}{2} \cdot 15 \cdot 4 = 7.5 \cdot 4 = 30 \text{ ft}^2
\]
Answer:
\[
\boxed{30}
\]
---
3)
Dimensions:
- \( b_1 = 11 \) yd
- \( b_2 = 8 \) yd
- \( h = 6 \) yd
Formula Application:
\[
A = \frac{1}{2} (b_1 + b_2) h = \frac{1}{2} (11 + 8) \cdot 6
\]
\[
A = \frac{1}{2} \cdot 19 \cdot 6 = 9.5 \cdot 6 = 57 \text{ yd}^2
\]
Answer:
\[
\boxed{57}
\]
---
4)
Dimensions:
- \( b_1 = 6 \) yd
- \( b_2 = 4 \) yd
- \( h = 5 \) yd
Formula Application:
\[
A = \frac{1}{2} (b_1 + b_2) h = \frac{1}{2} (6 + 4) \cdot 5
\]
\[
A = \frac{1}{2} \cdot 10 \cdot 5 = 5 \cdot 5 = 25 \text{ yd}^2
\]
Answer:
\[
\boxed{25}
\]
---
5)
Dimensions:
- \( b_1 = 7 \) in
- \( b_2 = 3 \) in
- \( h = 8 \) in
Formula Application:
\[
A = \frac{1}{2} (b_1 + b_2) h = \frac{1}{2} (7 + 3) \cdot 8
\]
\[
A = \frac{1}{2} \cdot 10 \cdot 8 = 5 \cdot 8 = 40 \text{ in}^2
\]
Answer:
\[
\boxed{40}
\]
---
6)
Dimensions:
- \( b_1 = 12 \) ft
- \( b_2 = 8 \) ft
- \( h = 9 \) ft
Formula Application:
\[
A = \frac{1}{2} (b_1 + b_2) h = \frac{1}{2} (12 + 8) \cdot 9
\]
\[
A = \frac{1}{2} \cdot 20 \cdot 9 = 10 \cdot 9 = 90 \text{ ft}^2
\]
Answer:
\[
\boxed{90}
\]
---
Final Answers:
1. \( \boxed{36} \)
2. \( \boxed{30} \)
3. \( \boxed{57} \)
4. \( \boxed{25} \)
5. \( \boxed{40} \)
6. \( \boxed{90} \)
These are the areas of the trapezoids in their respective units.
Parent Tip: Review the logic above to help your child master the concept of area of trapezoid worksheet pdf.
