Triangle Area Coverage: Calculate Tiles Needed for 10m × 8m Pool

Q: Why do we divide by 2 in the triangle area formula?

A triangle is exactly half of a rectangle with the same base and height. The formula $ \frac{base \times height}{2} $ accounts for this by cutting the rectangle area in half.

Q: How do I know which measurement is the base and which is the height?

For area calculations, it doesn't matter! Whether you use 10 × 8 ÷ 2 or 8 × 10 ÷ 2, you get the same result: 40 m².

Q: What if I get a decimal answer for the number of tiles?

In real situations, you'd round up to buy enough tiles. But if your math is correct for this problem, you should get exactly 10 tiles with no decimals.

Triangle Area Calculations with Tile Coverage

A hotel plans to build a special pool in its garden in the shape of a triangle.

The length of the pool 10 meters and its width 8 meters.

The pool is covered with tiles. The length of each tile is 2 meters and its width is 2 meters.

How many tiles do you need to cover the pool area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:16 Let's find out how many times a 2 meter square fits into triangle ABC.

00:22 First, we need to calculate the area of triangle ABC.

00:27 To do this, use the triangle area formula.

00:32 Multiply the height, called A C, by the base, called B C, and divide by 2.

00:38 Now, put the values into the formula and solve it step by step.

00:43 Great! This gives us the area of triangle ABC.

00:48 Next, let's look at our square tile.

00:52 We need to calculate its area.

00:55 Use the formula for a square's area.

00:59 Multiply Side, which is 2, by Side, which is 2, as well.

01:04 This gives us the area of our tile.

01:08 Now, divide the area of the triangle by the area of the square.

01:13 Put the values into the equation, and let's solve it.

01:17 And there you have it, this is your solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A hotel plans to build a special pool in its garden in the shape of a triangle.

The length of the pool 10 meters and its width 8 meters.

The pool is covered with tiles. The length of each tile is 2 meters and its width is 2 meters.

How many tiles do you need to cover the pool area?

Step-by-step solution

To find out how many tiles are needed we will calculate the triangular area and the area of each tile and then divide.

$\frac{\text{A.triángulo}}{A.baldosa}$

The result is equal to the number of tiles needed.

In a triangle its length is equal to its height and its width is equal to the base of the triangle

$\text{A.triangulo=}\frac{10\cdot8}{2}=40$

Given=h=length= $10$ meters

Given=base=width= $8$ meters

Given that the length is $2$ meters

The width: $2$ meters

Tile area $2\cdot2=4$

$\frac{40}{4}=10$

Final Answer

10 tiles

Key Points to Remember

Essential concepts to master this topic

Formula: Triangle area = $\frac{base \times height}{2}$
Technique: Divide total area by tile area: $\frac{40}{4} = 10$ tiles
Check: Verify 10 tiles × 4 m² each = 40 m² total triangle area ✓

Common Mistakes

Avoid these frequent errors

Using rectangle formula instead of triangle formula
Don't calculate 10 × 8 = 80 m² for triangle area! This treats the triangle as a rectangle and doubles the actual area. Always use triangle formula: $\frac{base \times height}{2}$ to get the correct 40 m².

Practice Quiz

Test your knowledge with interactive questions

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

FAQ

Everything you need to know about this question

Why do we divide by 2 in the triangle area formula?

A triangle is exactly half of a rectangle with the same base and height. The formula $\frac{base \times height}{2}$ accounts for this by cutting the rectangle area in half.

What if the tiles don't fit perfectly into the triangle shape?

In real life, you'd need to cut tiles to fit the slanted edge. But for math problems like this, we assume the tiles can be arranged to cover the exact area calculated: 40 square meters.

How do I know which measurement is the base and which is the height?

For area calculations, it doesn't matter! Whether you use 10 × 8 ÷ 2 or 8 × 10 ÷ 2, you get the same result: 40 m².

Can I solve this without calculating areas?

No, you need both areas to find how many tiles fit. Think of it as: How many 4 m² tiles fit into a 40 m² triangle? That's why we divide $\frac{40}{4} = 10$ .

What if I get a decimal answer for the number of tiles?

In real situations, you'd round up to buy enough tiles. But if your math is correct for this problem, you should get exactly 10 tiles with no decimals.

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Triangle Area Coverage: Calculate Tiles Needed for 10m × 8m Pool

Triangle Area Calculations with Tile Coverage

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we divide by 2 in the triangle area formula?

What if the tiles don't fit perfectly into the triangle shape?

How do I know which measurement is the base and which is the height?

Can I solve this without calculating areas?

What if I get a decimal answer for the number of tiles?

🌟 Unlock Your Math Potential

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