The problem asks us to solve three questions based on the provided image: 1. Identify the quadrilateral and find its perimeter. The quadrilateral has sides of 6 inches, 8 inches, 10 inches, and an unknown length.

1. Problem Description

The problem asks us to solve three questions based on the provided image:

1. Identify the quadrilateral and find its perimeter. The quadrilateral has sides of 6 inches, 8 inches, 10 inches, and an unknown length.

2. Find the area of the quadrilateral.

3. Find the area of the circle with a diameter of 14 cm, using $22/7$ for $\pi$.

2. Solution Steps

Question 18: Name the quadrilateral and find its perimeter.

The quadrilateral is a trapezoid because it has one pair of parallel sides. To find the perimeter, we need to determine the length of the fourth side. We can form a right triangle with the unknown side as the hypotenuse. The base of this right triangle is $10 - 8 = 2$ inches, and the height is 6 inches.

Using the Pythagorean theorem, we can find the length of the unknown side:

$c = \sqrt{a^2 + b^2}$

$c = \sqrt{2^2 + 6^2}$

$c = \sqrt{4 + 36}$

$c = \sqrt{40}$

$c = 2\sqrt{10}$ inches

Approximate value for $2\sqrt{10}$ is $2 \times 3.162 = 6.324$ inches.

The perimeter is the sum of all sides: $6 + 8 + 10 + 2\sqrt{10} = 24 + 2\sqrt{10}$ inches.

Question 19: Find the area of the quadrilateral.

The quadrilateral is a trapezoid, so its area can be calculated using the formula:

$Area = \frac{1}{2}(b_1 + b_2)h$

where $b_1$ and $b_2$ are the lengths of the parallel sides (bases) and $h$ is the height.

$Area = \frac{1}{2}(8 + 10) \times 6$

$Area = \frac{1}{2}(18) \times 6$

$Area = 9 \times 6$

$Area = 54$ square inches.

Question 20: Find the area of the circle. (use 22/7 for π)

The diameter of the circle is 14 cm, so the radius is half of that:

$r = \frac{14}{2} = 7$ cm

The area of a circle is given by the formula:

$Area = \pi r^2$

Using $\pi = \frac{22}{7}$:

$Area = \frac{22}{7} \times 7^2$

$Area = \frac{22}{7} \times 49$

$Area = 22 \times 7$

$Area = 154$ square cm.

3. Final Answer

1

8. The quadrilateral is a trapezoid and its perimeter is $24 + 2\sqrt{10}$ inches.

1

9. The area of the quadrilateral is 54 square inches.

2

0. The area of the circle is 154 square cm.