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To solve this problem, we need to find the lowest cost for covering the triangular area with tiles, using the information provided:

### Step 1: Calculate the Area of the Triangle
The triangle's dimensions are given:
- Height (\(h\)) = 350 cm
- Base (\(b\)) = 361.5 cm

The area (\(A\)) of a triangle is calculated by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
Substitute the given values:
\[
A = \frac{1}{2} \times 361.5 \, \text{cm} \times 350 \, \text{cm}
\]
\[
A = \frac{1}{2} \times 126525 \, \text{cm}^2
\]
\[
A = 63262.5 \, \text{cm}^2
\]

Since 1 square meter (m²) is equal to 10,000 cm², we convert the area to square meters:
\[
\text{Area in m}^2 = \frac{63262.5}{10000} = 6.32625 \, \text{m}^2
\]

### Step 2: Determine the Number of Tile Packs Needed
Each pack of tiles covers 1 m². Therefore, the number of packs required is:
\[
\text{Packs needed} = \lceil 6.32625 \rceil = 7 \, \text{packs}
\]
(We round up because we cannot purchase a fraction of a pack.)

### Step 3: Calculate the Cost with the Discount
The cost per pack is £35.95, and there is a one-third discount on each pack. First, calculate the discount amount:
\[
\text{Discounted price per pack} = 35.95 \times \left(1 - \frac{1}{3}\right)
\]
\[
= 35.95 \times \frac{2}{3} = 23.9667 \, \text{(approximately £23.97)}
\]

Now, multiply by the number of packs needed:
\[
\text{Total cost} = 7 \times 23.97 = 167.79
\]

### Answer
The lowest cost of the tiles is **£167.79**.

Would you like more details or have any questions on this solution?

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Here are 5 related questions for further practice:

1. What would the cost be if there were no discount applied to the tile packs?
2. How much area would be left uncovered if only 6 packs were purchased?
3. If the height of the triangle were doubled, how many packs would be needed?
4. How would the cost change if the discount was 50% instead of one-third?
5. What would be the total cost if the price per pack increased to £40.00?

**Tip:** Always double-check your unit conversions, especially when moving between square centimeters and square meters.

Dean wants to cover part of his floor, the part of the floor that needs covering is in the shape of a triangle like above. The tiles he wants to buy come in packs. Each pack covers 1 m² and costs £35.95. The tiles can be cut and joined. The pack is on offer with one third off the cost of the pack. Work out the lowest cost of the tiles.

Solve a practical problem involving the calculation of the lowest cost to cover a triangular floor area. Learn to find the area, convert units, determine the number of tile packs needed, and apply a percentage discount to the price. Ideal for students in Grades 9-10.

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