L4 · Surface area clinic

Learning goal

“I can choose and use the right 2-D model - net, orthographic drawing, or isometric drawing - to identify a right 3-D shape and compute its surface area, adjusting the face census to what a real problem actually covers.”

Orthographic drawing — a set of separate flat views of a 3-D shape: front view, top view, and right-side view, each a 2-D shape with the dimensions it sees. The three views together determine the shape's length, width, and height.

Isometric drawing — a single 2-D picture of a 3-D shape drawn on a dot grid so that the front, top, and one side are visible at once, as if looking at a corner. Good for recognizing a shape; awkward for measuring every face.

Worked example

An orthographic drawing of a right rectangular prism shows: front view a rectangle 6 cm wide by 4 cm high; top view a rectangle 6 cm wide by 3 cm deep; right-side view a rectangle 3 cm wide by 4 cm high. Step 1: Read the dimensions off the views: length 6, depth 3, height 4 (each dimension appears in two views - that is how the views confirm each other). Step 2: Choose the working model: to compute surface area, unfold mentally into a net - three face pairs. Step 3: SA = 2 x (6 x 3) + 2 x (6 x 4) + 2 x (3 x 4) = 36 + 48 + 24 = 108 cm2.

Check yourself — explain it

For finding surface area, the NET is the best of the three models because...

Paired problem — example still visible

An isometric drawing shows a cube whose edge, measured against the dot grid, is 3 cm. -> SA = 6 x 9 = 54 cm2

Faded completion — last step is yours

"Orthographic views of a prism: front 5 cm by 3 cm, top 5 cm by 2 cm, side 2 cm by 3 cm - so the prism is 5 by 2 by 3. SA = 2 x (5 x 2) + 2 x (5 x 3) + 2 x (2 x 3) = 20 + 30 + ___ = ___ cm2" -> 12; 62 cm2

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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