To find the surface area of a triangular prism, we need to calculate the area of all its faces and add them together.
Step 1: Identify the faces of the prism.
A triangular prism has 5 faces in total:
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2 Triangular bases: These are the front and back triangles.
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3 Rectangular sides: These connect the corresponding sides of the two triangles.
Step 2: Calculate the area of the two triangular bases.
The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.
- Base of the triangle = $6\text{ mm}$
- Height of the triangle = $4\text{ mm}$
$$ \text{Area of one triangle} = \frac{1}{2} \times 6 \times 4 = 12\text{ mm}^2 $$
Since there are two identical triangular bases:
$$ \text{Total area of triangles} = 12 \times 2 = 24\text{ mm}^2 $$
Step 3: Calculate the area of the three rectangular sides.
Each rectangle's length corresponds to the length of the prism ($9\text{ mm}$), and its width corresponds to one of the sides of the triangle. The sides of the triangle are given as $5\text{ mm}$, $5\text{ mm}$, and $6\text{ mm}$.
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Rectangle 1 (bottom): Width = $6\text{ mm}$, Length = $9\text{ mm}$
$$ \text{Area} = 6 \times 9 = 54\text{ mm}^2 $$
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Rectangle 2 (left side): Width = $5\text{ mm}$, Length = $9\text{ mm}$
$$ \text{Area} = 5 \times 9 = 45\text{ mm}^2 $$
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Rectangle 3 (right side): Width = $5\text{ mm}$, Length = $9\text{ mm}$
$$ \text{Area} = 5 \times 9 = 45\text{ mm}^2 $$
Step 4: Add all the areas together.
$$ \text{Total Surface Area} = (\text{Triangles}) + (\text{Rectangles}) $$
$$ \text{Total Surface Area} = 24 + 54 + 45 + 45 $$
$$ \text{Total Surface Area} = 24 + 144 $$
$$ \text{Total Surface Area} = 168\text{ mm}^2 $$
Final Answer:
168
Parent Tip: Review the logic above to help your child master the concept of triangular prisms surface area worksheet.
