Calculate Triangle Area: Paint Coverage in 6-Meter Square Playground

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

A triangle takes up exactly half the space of a rectangle with the same base and height. The formula $ \frac{1}{2} \times \text{base} \times \text{height} $ accounts for this!

Q: How do I identify the base and height from the diagram?

Look for the triangle's bottom edge (base) and the perpendicular distance from that edge to the opposite vertex (height). In this square, both are 6 meters.

Q: What if the triangle doesn't fit perfectly in the square?

The same formula works! Just measure the actual base and height of the triangle, regardless of the surrounding shape. The key is finding perpendicular measurements.

Q: Why does one paint bucket cover exactly one square meter?

This is given information in the problem. It creates a direct relationship: square meters of area = number of paint buckets needed. So 18 m² = 18 buckets.

Q: How can I double-check my triangle area calculation?

Visual check: Triangle should be half the square's areaMath check: Square area = 6² = 36, so triangle = 36 ÷ 2 = 18Formula check: $ \frac{1}{2} \times 6 \times 6 = 18 $ ✓

Triangle Area with Geometric Applications

In a square-shaped playground, they want to paint a part of it orange so that the shape of that color is a triangle.

The length of the playground is 6 meters.

one box of paint is required for each meter of paint.

How many buckets of paint do you need to paint the triangular area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine how many boxes are needed to paint the triangle area

00:03 Apply the formula to calculate the area of the triangle

00:07 (base x height) divided by 2

00:13 Substitute in the relevant values according to the given data and solve to find the area

00:18 This is the triangle's area

00:23 The area covered by one paint box

00:28 We'll divide the triangle area by the area covered by one paint box

00:31 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In a square-shaped playground, they want to paint a part of it orange so that the shape of that color is a triangle.

The length of the playground is 6 meters.

one box of paint is required for each meter of paint.

How many buckets of paint do you need to paint the triangular area?

Step-by-step solution

To solve this problem, we'll need to calculate the area of the triangle to determine the exact number of paint buckets required:

Step 1: Identify the base and height of the triangle.
The square's side length is 6 meters, and from the diagram, the triangle appears to have its base and height both as 6 meters.
Step 2: Calculate the area using the formula:
$\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$
Substituting the known values, we get:
$\frac{1}{2} \times 6 \times 6 = 18 \text{ square meters}$
Step 3: Determine the number of buckets needed.
One bucket of paint covers 1 square meter, so for 18 square meters, we need 18 buckets.

Therefore, the solution to the problem is $18 \text{ paint boxes}$ .

Final Answer

18 paint boxes

Key Points to Remember

Essential concepts to master this topic

Formula: Area of triangle = $\frac{1}{2} \times \text{base} \times \text{height}$
Calculation: $\frac{1}{2} \times 6 \times 6 = 18$ square meters
Verification: Check diagram shows triangle fills exactly half the 36 m² square ✓

Common Mistakes

Avoid these frequent errors

Using wrong triangle area formula
Don't use base × height = 6 × 6 = 36 square meters! This gives the area of the entire square, not the triangle. The triangle only covers half that space. Always use the correct formula: Area = ½ × base × height for triangles.

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 I divide by 2 in the triangle area formula?

A triangle takes up exactly half the space of a rectangle with the same base and height. The formula $\frac{1}{2} \times \text{base} \times \text{height}$ accounts for this!

How do I identify the base and height from the diagram?

Look for the triangle's bottom edge (base) and the perpendicular distance from that edge to the opposite vertex (height). In this square, both are 6 meters.

What if the triangle doesn't fit perfectly in the square?

The same formula works! Just measure the actual base and height of the triangle, regardless of the surrounding shape. The key is finding perpendicular measurements.

Why does one paint bucket cover exactly one square meter?

This is given information in the problem. It creates a direct relationship: square meters of area = number of paint buckets needed. So 18 m² = 18 buckets.

How can I double-check my triangle area calculation?

Visual check: Triangle should be half the square's area
Math check: Square area = 6² = 36, so triangle = 36 ÷ 2 = 18
Formula check: $\frac{1}{2} \times 6 \times 6 = 18$ ✓

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Calculate Triangle Area: Paint Coverage in 6-Meter Square Playground

Triangle Area with Geometric Applications

❤️ 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 I divide by 2 in the triangle area formula?

How do I identify the base and height from the diagram?

What if the triangle doesn't fit perfectly in the square?

Why does one paint bucket cover exactly one square meter?

How can I double-check my triangle area calculation?

🌟 Unlock Your Math Potential

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