Answer:
1. Left side = 3 inches, Bottom side = 4 inches, Right side = 2 inches, Top side = 5 inches
2. A = 6 inches²
3. A = 8 inches²
4. A = 10 inches²
5. A = 12 inches²
6. A = 36 inches²
7. Left side = 5 cm, Bottom side = 12 cm, Right side = 4 cm, Top side = 13 cm
8. A = 180 cm²
Explanation:
1. Label the dimensions of the prism:
Left side = 3 inches
Bottom side = 4 inches
Right side = 2 inches
Top side = 5 inches
2. Area of the red rectangle:
Formula:
LH = A (Length x Height = Area)
A = 3 x 2
A = 6 inches²
3. Area of the blue rectangle:
Formula:
LH = A (Length x Height = Area)
A = 4 x 2
A = 8 inches²
4. Area of the green rectangle:
Formula:
LH = A (Length x Height = Area)
A = 5 x 2
A = 10 inches²
5. (They gave the formula of the two triangles, but the question said green rectangle? They must've meant yellow triangles)
Area of the yellow triangles:
Formula:
2 (1/2 Bh) (2 (half of base x height))
A = 2(1/2 3 x 4)
A = 2(1/2 12)
A = 2(6)
A = 12 inches²
6. Total surface area of the triangular prism:
Formula:
LH + LH + LH + 2 (1/2 Bh) = Surface Area of the triangular prism (Area of the red rectangle + Area of the blue rectangle + Area of the green rectangle + Area of the yellow triangles = Total surface area of the triangular prism)
A = 6 inches² + 8 inches² + 10 inches² + 12 inches²
A = 36 inches²
7. Label the dimensions of the prism:
Left side = 5 cm
Bottom side = 12 cm
Right side = 4 cm
Top side = 13 cm
8. Total surface area of the triangular prism:
First, we can find the area of each shape, as we had previously to find the total area of the net and the surface area of the triangular prism.
Area of the red rectangle:
Formula:
LH = A (Length x Height = Area)
A = 5 x 4
A = 20 cm²
Area of the blue rectangle:
Formula:
LH = A (Length x Height = Area)
A = 12 x 4
A = 48 cm²
Area of the green rectangle:
Formula:
LH = A (Length x Height = Area)
A = 13 x 4
A = 52 cm²
Area of the yellow triangles:
Formula:
2 (1/2 Bh) (2 (half of base x height))
A = 2(1/2 5 x 12)
A = 2(1/2 60)
A = 2(30)
A = 60 cm²
Total surface area of the triangular prism:
LH + LH + LH + 2 (1/2 Bh) = Surface Area of the triangular prism (Area of the red rectangle + Area of the blue rectangle + Area of the green rectangle + Area of the yellow triangles = Total surface area of the triangular prism)
A = 20 cm² + 48 cm² + 52 cm² + 60 cm²
A = 180 cm²