Problem: Calculate the areas of the given triangles and quadrilaterals.
####
Step-by-Step Solution:
---
1. Trapezoid (Problem 1)
Given:
- Bases: \(4.16\) and \(7\)
- Height: \(3\)
Formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
Substitute the values:
\[
\text{Area} = \frac{1}{2} \times (4.16 + 7) \times 3
\]
Calculate step-by-step:
\[
4.16 + 7 = 11.16
\]
\[
\frac{1}{2} \times 11.16 = 5.58
\]
\[
5.58 \times 3 = 16.74
\]
Answer:
\[
\boxed{16.74}
\]
---
2. Triangle (Problem 2)
Given:
- Base: \(3.00\)
- Height: \(4\)
Formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Substitute the values:
\[
\text{Area} = \frac{1}{2} \times 3.00 \times 4
\]
Calculate step-by-step:
\[
\frac{1}{2} \times 3.00 = 1.5
\]
\[
1.5 \times 4 = 6.00
\]
Answer:
\[
\boxed{6.00}
\]
---
3. Trapezoid (Problem 3)
Given:
- Bases: \(7.97\) and \(17\)
- Height: \(3\)
Formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
Substitute the values:
\[
\text{Area} = \frac{1}{2} \times (7.97 + 17) \times 3
\]
Calculate step-by-step:
\[
7.97 + 17 = 24.97
\]
\[
\frac{1}{2} \times 24.97 = 12.485
\]
\[
12.485 \times 3 = 37.455
\]
Answer:
\[
\boxed{37.46} \quad \text{(Rounded to two decimal places)}
\]
---
4. Parallelogram (Problem 4)
Given:
- Base: \(8\)
- Height: \(2.88\)
Formula for the area of a parallelogram:
\[
\text{Area} = \text{Base} \times \text{Height}
\]
Substitute the values:
\[
\text{Area} = 8 \times 2.88
\]
Calculate step-by-step:
\[
8 \times 2.88 = 23.04
\]
Answer:
\[
\boxed{23.04}
\]
---
5. Rectangle (Problem 5)
Given:
- Length: \(11\)
- Width: \(5\)
Formula for the area of a rectangle:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
Substitute the values:
\[
\text{Area} = 11 \times 5
\]
Calculate step-by-step:
\[
11 \times 5 = 55
\]
Answer:
\[
\boxed{55}
\]
---
6. Triangle (Problem 6)
Given:
- Base: \(14\)
- Height: \(6.75\)
Formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Substitute the values:
\[
\text{Area} = \frac{1}{2} \times 14 \times 6.75
\]
Calculate step-by-step:
\[
\frac{1}{2} \times 14 = 7
\]
\[
7 \times 6.75 = 47.25
\]
Answer:
\[
\boxed{47.25}
\]
---
Final Answers:
1. \(\boxed{16.74}\)
2. \(\boxed{6.00}\)
3. \(\boxed{37.46}\)
4. \(\boxed{23.04}\)
5. \(\boxed{55}\)
6. \(\boxed{47.25}\)
Parent Tip: Review the logic above to help your child master the concept of area of triangle worksheet.
