Fill in the blank to complete the formula for the surface area of a triangular prism.
Replace "Blank" With the answer.
The surface area of a triangular prism is S.A=Blank+(S³+S³+S³)Blank
The surface area of a triangular prism is S.A = (base perimeter) + (Sum of the areas of the three rectangular faces)
To fill in the blank and complete the formula for the surface area of a triangular prism, let's go through the steps.
A triangular prism has two triangular bases and three rectangular faces. The formula for the surface area is the sum of the areas of these five faces.
1. Start by finding the area of each triangular base. The formula for the area of a triangle is (base × height) ÷ 2. Let's call the base of the triangle B1 and its height H1.
2. The surface area also includes the areas of the three rectangular faces. Each rectangular face has a length equal to the base B1 of the triangle and height equal to the height H2 of the prism. The formula for the area of a rectangle is length × width. Therefore, the total area of the three rectangular faces is 3 × B1 × H2.
3. Now, we can write the complete formula for the surface area of a triangular prism:
Surface Area (S.A) = (Area of triangular base 1) + (Area of triangular base 2) + (Area of three rectangular faces)
Given that the formula you provided is:
S.A = Blank + (S³ + S³ + S³) × Blank
We can replace the "Blank" with the solutions we found above:
S.A = (B1 × H1) + (B1 × H1) + 3(B1 × H2)
Hence, the completed formula for the surface area of a triangular prism would be:
S.A = 2(B1 × H1) + 3(B1 × H2)