Question

10 the diagram shows one face of a wall. this face is in the shape of a pentagon with exactly one line of symmetry. omondi is going to paint this face of the wall once. he has to buy all the paint that he needs to use. the paint in each tin of paint omondi is going to buy will cover 16m² of the face of the wall. work out the least number of tins of paint omondi will need to buy. show your working clearly.

Explanation:

Step1: Split shape into rectangle + triangle

The pentagon can be divided into a rectangle (base 10m, height 6m) and an isosceles triangle (base 10m, equal sides 7m).

Step2: Calculate rectangle area

Area of rectangle = length × width
$\text{Area}_{\text{rectangle}} = 10 \times 6 = 60 \, \text{m}^2$

Step3: Find triangle height

Use Pythagoras on half the triangle: base half = $\frac{10}{2}=5$m, hypotenuse 7m.
$h = \sqrt{7^2 - 5^2} = \sqrt{49 - 25} = \sqrt{24} \approx 4.899 \, \text{m}$

Step4: Calculate triangle area

Area of triangle = $\frac{1}{2} \times \text{base} \times \text{height}$
$\text{Area}_{\text{triangle}} = \frac{1}{2} \times 10 \times 4.899 \approx 24.495 \, \text{m}^2$

Step5: Total wall area

Add rectangle and triangle areas.
$\text{Total Area} = 60 + 24.495 = 84.495 \, \text{m}^2$

Step6: Calculate number of tins

Divide total area by coverage per tin, round up.
$\text{Number of tins} = \lceil \frac{84.495}{16}
ceil = \lceil 5.281
ceil = 6$

Answer:

6