Let’s solve each problem step by step. We’ll start with Section A (nets) and then move to Section B (3D objects). Remember: surface area is the total area of all faces added together.
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Section A: Work out the area of the nets
These are flat patterns that fold into prisms. We just add up the areas of all the rectangles and triangles shown.
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A1)
This net has:
- Two small squares: 2 cm × 2 cm → each is 4 cm² → total = 8 cm²
- Four long rectangles: each is 10 cm × 2 cm → each is 20 cm² → total = 80 cm²
Wait — let’s look again. Actually, looking at the diagram:
It looks like a rectangular prism net. The central part is a rectangle 10 cm wide and 2 cm tall. Then there are flaps on top, bottom, left, right.
Actually, better way: count all visible shapes.
From the drawing:
- Top flap: 10 cm × 2 cm = 20 cm²
- Bottom flap: same = 20 cm²
- Left side: 2 cm × 2 cm? Wait no — actually, the horizontal parts are 10 cm long, vertical parts are 2 cm high.
Actually, standard cross-shaped net for a rectangular prism:
There are 6 faces:
- Front/back: 10 cm × 2 cm → two of them → 2 × 20 = 40 cm²
- Left/right: 2 cm × 2 cm → two of them → 2 × 4 = 8 cm²
- Top/bottom: 10 cm × 2 cm → wait, that would be same as front/back? That can’t be.
Wait — maybe I misread. Let me re-express based on typical net layout.
Looking at diagram 1):
The center rectangle is 10 cm wide and 2 cm high. Above it is another 10x2, below it another 10x2. To the left and right of the center are 2x2 squares.
So:
- Three horizontal rectangles: each 10×2 = 20 → 3 × 20 = 60
- Two side squares: each 2×2 = 4 → 2 × 4 = 8
Total = 60 + 8 =
68 cm²
But wait — that’s only 5 faces? A prism should have 6. Oh! The third horizontal one might be missing? No — in the diagram, it shows three horizontal strips and two side squares — that’s 5 pieces. But when folded, the “side
Parent Tip: Review the logic above to help your child master the concept of surface area and volume worksheets.
