Note: This is the Solution of review exercise 9.4 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 9.4
Question # 01:
\( (i) \; \)What is the sum of the interior angles of a decagon (10-sided polygon)?
\( (ii) \; \)Calculate the measure of each interior angle of a regular hexagon.
\( (iii) \; \)What is each exterior angle of a regular pentagon?
\( (iv) \; \)If the sum of the interior angles of a polygon is \(1440^\circ\), how many sides does the polygon have?
Question 2: In a parallelogram \(\small{ABCD}\), \(\small{m\overline{AB}=10\ cm}\), \(\small{m\overline{AD}=6\ cm}\) and \(\small{m\angle BAD=45^\circ}\). Calculate the length of diagonal \(\small{m\overline{AC}}\).
Question 3: In a parallelogram \(\small{ABCD}\) if \(\small{m\angle DAB=70^\circ}\), find the measures of all other angles in the parallelogram.
Question 4: A shape is created by cutting a square in half diagonally and then attaching a right-angled triangle to the hypotenuse of each half. Explain why this shape can tessellate and calculate the interior angle of the new shape.
Question 5: A tessellation is created by repeatedly reflecting a basic shape. The basic shape is right-angled triangle with sides of length \(\small{3,4}\) and \(\small{5}\) units. Find: The minimum number of reflections needed to create a tessellation that covers a square with an area of \(\small{3600}\) square units.
Question 6: A tessellation is created using regular hexagons. Each hexagon has a side length of \(\small{5\ cm}\). Find the total area of the tessellation if it consists of \(\small{25}\) hexagons and total perimeter of the outer edge of the tessellation, assuming it’s a perfect hexagon.
Question 7: A rectangular floor is \(\small{12\ m}\) by \(\small{15\ m}\). How many square tiles, each \(\small{1\ m}\) by \(\small{1\ m}\), are needed to cover the floor?
Question 8: A rectangular wall has a length of \(\small{10\ m}\) tall and \(\small{12\ m}\) wide. How many gallons of paint are needed to cover the wall, if one gallon covers \(\small{350\ m^2}\).
Question 9: A rectangular wall has a length of \(\small{10\ m}\) and a width of \(\small{4}\) meters. If \(\small{1}\) liter of paint covers \(\small{2\ m^2}\), how many liters of paint are needed to cover the wall?
Question 10: A window has a trapezoidal shape with parallel sides of \(\small{3\ m}\) and \(\small{1.5\ m}\) and a height of \(\small{2\ m}\). Find the area of the window.
