Step-by-step explanation:
I answered this already yesterday.
the composite figure is actually the combination of 2 figures :
1. a 7cm × 6cm × 2cm box (purple)
2. a 8cm × 7cm × 6cm triangular shaped half-box (pink) with 10cm length of the rectangular "roof".
2 sides are completely blocking each other, so they are not part of the combined surface area.
let's start with the purple box. its contribution to the surface area is :
top and bottom 7×2 rectangles
front and back 6×2 rectangles
no left (blocked by the half-box)
right 6×7 rectangle
so, we get
2 × 7×2 = 2×14 = 28 cm²
2 × 6×2 = 2×12 = 24 cm²
6×7 = 42 cm²
in total that is : 94 cm²
the half-box contributes to the surface area :
top 10×7 rectangle
bottom 8×7 rectangle
front and back 8×6/2 triangles
no left (due to the triangular shape)
no right (blocked by the box)
so, we get
10×7 = 70 cm²
8×7 = 56 cm²
2 × 8×6/2 = 2×24 = 48 cm²
in total that is : 174 cm²
and so, the total surface area of the composite figure is
174 + 94 = 268 cm²
