find surface area of composite shapes

Question

https://ibb.co/G30kvLvg

Answer 1

1. Understand the Shape

The shape is made up of:

1. A rectangular prism (box): 8 cm wide × 6 cm tall × 5 cm deep
2. A triangular prism on top (roof): triangle base 8 cm, height 4 cm, depth 5 cm

2. Find Surface Areas of Each Part

A) Floor

1. One rectangle:
2. 8 × 5 = 40 cm²

B) Front and Back Walls

1. Two rectangles:
2. 2 × (6 × 8) = 2 × 48 = 96 cm²

C) Side Walls

1. Two rectangles:
2. 2 × (6 × 5) = 2 × 30 = 60 cm²

D) Triangular Ends (front and back of roof)

1. One triangle: (1/2) × 8 × 4 = 16 cm²
2. Two triangles: 2 × 16 = 32 cm²

E) Slanted Roof Sides

1. First, find the slant height using the Pythagorean Theorem:
2. slant height = √(4² + 4²) = √32 = 4√2 ≈ 5.66 cm
3. One slanted rectangle: 5.66 × 5 = 28.3 cm²
4. Two slanted rectangles: 2 × 28.3 = 56.6 cm²

3. Add All the Areas Together

1. Floor: 40
2. Front & Back Walls: 96
3. Side Walls: 60
4. Triangles: 32
5. Slanted Roof Rectangles: 56.6

Total Surface Area = 40 + 96 + 60 + 32 + 56.6 = 284.6 cm²

Answer 2

You have different triangles and rectangles. Find the areas and add them

Floor: 8x5

Front and back walls: 2 x (6 x 8)

Side walls: 2 x (5 x 6)

Triangles: 2 x(.5*4 x 8)

Roof Rectangles: 2 * slant height * 5 Slant height = sqrt(4^2 + 4^2) =4sqrt(2)