8. Assessment Questions

1. Find the area of a trapezium with parallel sides 8cm and 12cm, height 5cm.

To find the area of a trapezium (also called a trapezoid), you can use the formula:

where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height. In this case, the lengths of the parallel sides are 8 cm and 12 cm, and the height is 5 cm.

1. Add the lengths of the parallel sides:
   • 8 cm + 12 cm = 20 cm
2. Multiply the sum by the height:
   • 20 cm × 5 cm = 100 cm²
3. Divide by 2:
   • 100 cm² ÷ 2 = 50 cm².

So, the area of the trapezium is 50 cm².

Imagine a trapezium-shaped garden bed where the top is wider than the bottom. If the top is 12 cm wide, the bottom 8 cm, and it's 5 cm tall, calculating its area helps you understand how much soil is needed to fill it or how many plants can be placed in it.

2. Calculate the volume of a cylinder with radius 7cm and height 10cm.

To find the volume of a cylinder, the formula is:

where $r$ is the radius and $h$ is the height. In this example:

1. Find the area of the base (circle):
   • $r^2 = (7 \text{cm})^2 = 49 \text{cm}^2$
   • So, Area = $\pi \times 49 \approx 3.14 \times 49 \approx 153.86 \text{cm}^2$
2. Multiply by the height:
   • Volume = 153.86 cm² × 10 cm = 1538.6 cm³.

Therefore, the volume of the cylinder is approximately 1538.6 cm³.

Think about a tall, cylindrical glass. If the glass has a radius of 7 cm and a height of 10 cm, the volume tells you how much liquid it can hold. So, if you want to pour juice into this glass, about 1538.6 cm³ of juice fits inside!

3. How many 25cm × 25cm tiles needed for a 4m × 5m floor?

First, convert the dimensions of the floor from meters to centimeters since the tile dimensions are given in centimeters:

Next, calculate the area of the floor:

1. Floor Area = Length × Width = 400 cm × 500 cm = 200,000 cm².
2. Calculate the area of one tile:
   • Tile Area = 25 cm × 25 cm = 625 cm².
3. Now, to find the number of tiles, divide the total area of the floor by the area of one tile:
   • $\text{Number of tiles} = \frac{200,000 \text{ cm}^2}{625 \text{ cm}^2} = 320 \text{ tiles}.$

Thus, you would need 320 tiles to cover the entire floor.

Imagine you're tiling your bathroom floor. Knowing that each tile covers a small area, you can find out how many such small tiles are needed to cover the entire floor area. Here, for a floor of size 4m × 5m, you need enough tiles to fill it without any gaps!

--