Question

section 3: quadrilaterals & polygons

1. what is the sum of the interior angles of a quadrilateral?
2. how many sides does a pentagon have?
3. what is a four - sided polygon with opposite sides parallel and equal?
4. what do you call a quadrilateral with one pair of parallel sides?
5. what is the name of a regular polygon with 8 sides?
6. find the area of a rectangle with length 12 cm and width 5 cm.

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a quadrilateral, \(n = 4\).

Step2: Calculate the sum of interior angles

Substitute \(n = 4\) into the formula: \((4 - 2)\times180^{\circ}=2\times180^{\circ} = 360^{\circ}\).

Step3: Answer question 22

A pentagon has \(5\) sides.

Step4: Answer question 23

A four - sided polygon with opposite sides parallel and equal is a parallelogram.

Step5: Answer question 24

A quadrilateral with one pair of parallel sides is a trapezoid.

Step6: Answer question 25

A regular polygon with 8 sides is called an octagon.

Step7: Calculate the area of the rectangle (question 26)

The formula for the area of a rectangle is \(A=\text{length}\times\text{width}\). Given length \(l = 12\mathrm{cm}\) and width \(w = 5\mathrm{cm}\), then \(A=12\times5=60\mathrm{cm}^{2}\).

Answer:

1. \(360^{\circ}\)
2. \(5\)
3. Parallelogram
4. Trapezoid
5. Octagon
6. \(60\mathrm{cm}^{2}\)