Worksheets with areas and perimeters of polygons and shapes, made ... - Free Printable

The image you uploaded is a worksheet titled "Perimeter and Area," which asks students to calculate the perimeter and area of various triangles. Below, I will explain how to solve these problems step by step using general formulas for triangles.

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General Formulas for Triangles

1. Perimeter:
The perimeter of a triangle is the sum of the lengths of its three sides.
\[
\text{Perimeter} = a + b + c
\]
where \(a\), \(b\), and \(c\) are the lengths of the sides of the triangle.

2. Area:
The area of a triangle can be calculated using the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the "base" is one side of the triangle, and the "height" is the perpendicular distance from the base to the opposite vertex.

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Step-by-Step Solution

#### Example Problem (Generic Triangle)
Let's assume we have a triangle with the following dimensions:
- Base (\(b\)) = 6 units
- Height (\(h\)) = 4 units
- Side lengths: \(a = 5\) units, \(b = 6\) units, \(c = 7\) units

#### Step 1: Calculate the Perimeter
Using the formula for the perimeter:
\[
\text{Perimeter} = a + b + c
\]
Substitute the given side lengths:
\[
\text{Perimeter} = 5 + 6 + 7 = 18 \text{ units}
\]

#### Step 2: Calculate the Area
Using the formula for the area:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Substitute the given base and height:
\[
\text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square units}
\]

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Applying to the Worksheet

For each triangle in the worksheet:
1. Identify the side lengths to calculate the perimeter.
2. Identify the base and height to calculate the area.

#### Sample Calculations for Specific Triangles
1. Triangle 1:
- Side lengths: \(a = 3\), \(b = 4\), \(c = 5\)
- Base (\(b\)) = 4, Height (\(h\)) = 3
- Perimeter: \(3 + 4 + 5 = 12\) units
- Area: \(\frac{1}{2} \times 4 \times 3 = 6\) square units

2. Triangle 2:
- Side lengths: \(a = 5\), \(b = 5\), \(c = 8\)
- Base (\(b\)) = 8, Height (\(h\)) = 3
- Perimeter: \(5 + 5 + 8 = 18\) units
- Area: \(\frac{1}{2} \times 8 \times 3 = 12\) square units

3. Triangle 3:
- Side lengths: \(a = 6\), \(b = 8\), \(c = 10\)
- Base (\(b\)) = 8, Height (\(h\)) = 6
- Perimeter: \(6 + 8 + 10 = 24\) units
- Area: \(\frac{1}{2} \times 8 \times 6 = 24\) square units

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Final Answer

For each triangle on the worksheet, follow the steps above to calculate the perimeter and area. The specific answers will depend on the dimensions provided for each triangle. If you need help with a particular triangle, let me know!

\[
\boxed{\text{Use the formulas: Perimeter = } a + b + c \text{ and Area = } \frac{1}{2} \times \text{base} \times \text{height}}
\]