what is the perimeter and area of a trapezoid if the:  the leg=31.6, altitude=10, base (bottom) = 70, base (top) = 10

To find the perimeter and area of the trapezoid, we'll use the following formulas:

### 1. Area of a Trapezoid:
The area \( A \) of a trapezoid can be found using the formula:
\[
A = \frac{1}{2} \times ( \text{Base}_1 + \text{Base}_2 ) \times \text{Height}
\]
where:
- \(\text{Base}_1 = 70\) (bottom base)
- \(\text{Base}_2 = 10\) (top base)
- \(\text{Height} = 10\) (altitude)

### 2. Perimeter of a Trapezoid:
The perimeter \( P \) of a trapezoid is the sum of all its sides:
\[
P = \text{Base}_1 + \text{Base}_2 + \text{Leg}_1 + \text{Leg}_2
\]
where the two legs are equal in this case:
- \(\text{Leg}_1 = \text{Leg}_2 = 31.6\)

#### Step 1: Calculate the Area
\[
A = \frac{1}{2} \times (70 + 10) \times 10 = \frac{1}{2} \times 80 \times 10 = 400 \text{ square units}
\]

#### Step 2: Calculate the Perimeter
\[
P = 70 + 10 + 31.6 + 31.6 = 143.2 \text{ units}
\]

### Final Answers:
- **Area:** \( 400 \) square units
- **Perimeter:** \( 143.2 \) units

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How does changing the height of a trapezoid affect its area?
2. What is the perimeter if one leg was 35 units instead of 31.6 units?
3. Can you find the area of an isosceles trapezoid given only the bases and height?
4. How would you calculate the area of a trapezoid using the median instead of the height?
5. What are some practical applications of calculating the area of a trapezoid?

**Tip:** When solving problems involving trapezoids, always make sure to identify whether the trapezoid is isosceles, as this can simplify the perimeter calculations.

Learn how to calculate the perimeter and area of a trapezoid with given dimensions: base = 70, top base = 10, and altitude = 10. Understand the formulas used for area and perimeter calculations, with step-by-step solutions.

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