https://file.aiquickdraw.com/mathbot/file/1725634105044kx8s8fyw.jpg

I'll analyze the content of the uploaded image and extract the mathematical questions for solving.

### The image contains the following questions:

1. **Calculate the perimeter of the trapezium**:
   - The diagram shows a trapezium with side lengths given as \(7 \, \text{cm}\), \(12 \, \text{cm}\), \(4 \, \text{cm}\), and \(6 \, \text{cm}\).

2. **A circle diagram** with:
   - A line \(AB = 14 \, \text{cm}\), which is the diameter of the circle.
   
   (a) **State the special name for line AB**:
   - We need to provide the term for a line segment that passes through the center of a circle and whose endpoints lie on the circle.
   
   (b) **Calculate the circumference of the circle** (using \(\pi = \frac{22}{7}\)).
   - Given the diameter \(AB = 14 \, \text{cm}\), we calculate the circumference.

   (c) **Find the area of the circle** (use \(\pi = \frac{22}{7}\)).
   - Using the same diameter \(AB = 14 \, \text{cm}\), we calculate the area of the circle.

---

### Let's start with the solutions:

#### 1. **Perimeter of the trapezium**:
The perimeter of a trapezium is the sum of the lengths of all its sides. The given side lengths are \(7 \, \text{cm}\), \(12 \, \text{cm}\), \(4 \, \text{cm}\), and \(6 \, \text{cm}\).

\[
\text{Perimeter} = 7 + 12 + 4 + 6 = 29 \, \text{cm}
\]

#### 2. **Circle-related questions**:

(a) **Special name for line AB**:
Since \(AB\) passes through the center of the circle and its endpoints lie on the circle, \(AB\) is the **diameter** of the circle.

(b) **Circumference of the circle**:
The formula for the circumference of a circle is:
\[
C = \pi d
\]
where \(d = 14 \, \text{cm}\) is the diameter and \(\pi = \frac{22}{7}\).

\[
C = \frac{22}{7} \times 14 = 44 \, \text{cm}
\]

(c) **Area of the circle**:
The formula for the area of a circle is:
\[
A = \pi r^2
\]
where \(r\) is the radius. The radius is half of the diameter, so \(r = \frac{14}{2} = 7 \, \text{cm}\). Using \(\pi = \frac{22}{7}\):

\[
A = \frac{22}{7} \times 7^2 = \frac{22}{7} \times 49 = 154 \, \text{cm}^2
\]

---

Let me know if you'd like further details or clarifications. Here are 5 related questions you can explore:

1. How would the perimeter change if one of the trapezium's sides increased by 2 cm?
2. What would be the radius of a circle if its circumference is 50 cm?
3. Can you calculate the area of a semicircle with diameter 14 cm?
4. What is the relation between the diameter and the radius of a circle?
5. How do you find the height of a trapezium if its area is given?

**Tip:** When dealing with circles, remember that the diameter is always twice the radius, which simplifies many calculations.

Calculate the perimeter of a trapezium with side lengths of 7 cm, 12 cm, 4 cm, and 6 cm. Additionally, a circle is shown with a diameter of 14 cm, and several related questions are posed, including identifying the special name for the line AB, calculating the circumference, and determining the area.

Solve the problem of finding the perimeter of a trapezium with side lengths of 7 cm, 12 cm, 4 cm, and 6 cm. Additionally, calculate the circumference and area of a circle with a diameter of 14 cm. Learn the properties of circles and trapeziums, suitable for Grades 6-8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation