Day 119Choosing Area Volume or Surface Area

Build the idea

Read the requested quantity first and identify the relevant model. Two matching triangles form a parallelogram, so A = (base × perpendicular height)/2. A slanted side is not necessarily the height. Label area in square units. Explain why the units and the final value fit the situation.

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

1. Sketch a triangle with base 16 cm and perpendicular height 3 cm. Find its area.

2. A rectangular prism has edges 6, 1, and 5 cm. Sketch it and find its volume.

3. A 6 cm by 2 cm base and 2 cm height form a closed box. Draw its net and find the material area. Ignore tabs and overlap.

4. An L-shaped garden is a 11 m by 11 m rectangle with an 7 m by 7 m corner rectangle removed. Sketch and find the garden area.

5. A square pyramid has base edge 8 cm. Each triangular face has perpendicular face height 7 cm. Draw a net and calculate total surface area.

6. Sketch a triangle with base 8 cm and perpendicular height 2 cm. Find its area.

7. A rectangular prism has edges 2 1/2, 2 1/2, and 3 cm. Sketch it and find its volume. Show both lwh and Bh.

8. A 4 cm by 7 cm base and 3 cm height form an open-top box. Draw its net and find the material area. Ignore tabs and overlap.

9. A 11 m by 7 m rectangle has a right-triangle corner removed with perpendicular legs 3 m and 4 m. Sketch the remaining polygon and find its area.

10. A square pyramid has base edge 14 cm. Each triangular face has perpendicular face height 10 cm. Draw a net and calculate total surface area. Explain why the vertical pyramid height is not needed.