Find the surface area of the solid figure with an equilateral triangle base.

Question

triangle base h= 3.9 cm and one side of the base= 4.5 cm
the height of a face= 3.5 cm

Answer 1

To find the surface area of the solid figure with an equilateral triangle base, you first need to find the area of the triangle base and then calculate the area of the three triangular faces.

1. Area of the equilateral triangle base:
Since the base is an equilateral triangle with side length 4.5 cm, we can use the formula for the area of an equilateral triangle: A = (sqrt(3) / 4) * s^2, where s is the side length.
A = (sqrt(3) / 4) * (4.5)^2
A = (sqrt(3) / 4) * 20.25
A ≈ 9.836 cm^2

2. Surface area of the three triangular faces:
Since the height of each face is 3.5 cm, the area of each triangular face is: (1/2) * base * height.
Area of each triangular face = (1/2) * 4.5 * 3.5
Area of each triangular face ≈ 7.875 cm^2

Now, we have three identical triangular faces, so the total surface area of the three faces is:
Total area of the three triangular faces = 3 * 7.875
Total area of the three triangular faces ≈ 23.625 cm^2

3. Total surface area of the solid figure:
To find the total surface area of the solid figure, you need to add the area of the equilateral triangle base to the total area of the three triangular faces:
Total surface area = area of the base + total area of the three faces
Total surface area ≈ 9.836 + 23.625
Total surface area ≈ 33.461 cm^2

Therefore, the surface area of the solid figure with an equilateral triangle base is approximately 33.461 cm^2.