Question

1. find the perimeter of a square with side 7 cm.
2. what is the area of a parallelogram with base 10 cm and height 4 cm?
3. what is the sum of the interior angles of a hexagon?
4. true or false: all rectangles are parallelograms.

section 4: circles

1. what is the distance around a circle called?
2. what is the distance across a circle through its center called?
3. what do we call a line that touches a circle at exactly one point?
4. what is the formula for the area of a circle?
5. find the circumference of a circle with radius 5 cm. (use π = 3.14)

Explanation:

Step1: Perimeter of square formula

Perimeter of square \(P = 4\times side\). Given side \(a = 7\) cm. So \(P=4\times7\).

Step2: Calculate perimeter

\(P = 28\) cm.

Step3: Area of parallelogram formula

Area of parallelogram \(A=base\times height\). Given base \(b = 10\) cm and height \(h = 4\) cm. So \(A = 10\times4\).

Step4: Calculate area

\(A=40\) \(cm^{2}\).

Step5: Sum of interior angles formula

Sum of interior angles of a polygon \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a hexagon \(n = 6\). So \(S=(6 - 2)\times180^{\circ}\).

Step6: Calculate sum

\(S = 720^{\circ}\).

Step7: Rectangle and parallelogram properties

A rectangle has opposite sides equal and parallel (properties of a parallelogram). So the statement "All rectangles are parallelograms" is True.

Step8: Circle - distance around

The distance around a circle is called circumference.

Step9: Circle - distance across through center

The distance across a circle through its center is called diameter.

Step10: Line touching circle at one point

A line that touches a circle at exactly one point is called a tangent.

Step11: Area of circle formula

The formula for the area of a circle is \(A=\pi r^{2}\), where \(r\) is the radius.

Step12: Circumference formula

Circumference \(C = 2\pi r\). Given \(r = 5\) cm and \(\pi=3.14\). So \(C=2\times3.14\times5\).

Step13: Calculate circumference

\(C = 31.4\) cm.

Answer:

1. \(28\) cm
2. \(40\) \(cm^{2}\)
3. \(720^{\circ}\)
4. True
5. Circumference
6. Diameter
7. Tangent
8. \(A=\pi r^{2}\)
9. \(31.4\) cm