Find the area of the white space in each composite shape on this Grade 6 Area Worksheet.

Explanation:
We are asked to find the area of the white space in each figure. That means we need to subtract the area of any black (shaded) shape from the total area of the whole figure — or, if the white space is made of separate shapes, add up those areas directly.

Let’s go one by one.

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Problem 1:
The figure is a rectangle (10 m long × 6 m tall) attached to a triangle on the right side. The triangle has base = 6 m (same as height of rectangle), and height = 5 m (given horizontally). The entire figure is white — there’s no black shading. So the white space is just the whole shape.

- Area of rectangle = length × width = 10 m × 6 m = 60 m²
- Area of triangle = (base × height) ÷ 2 = (6 m × 5 m) ÷ 2 = 30 ÷ 2 = 15 m²
- Total white area = 60 + 15 = 75 m²

✔ Double-check: Yes, no black part — all white.

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Problem 2 (first one labeled “2”):
A rectangle 12 m wide × 8 m tall, with a black triangle inside it. The triangle’s base is 6 m (horizontal), and its height is the full height of the rectangle = 8 m (vertical), since the triangle goes from top to bottom.

- Total rectangle area = 12 × 8 = 96 m²
- Black triangle area = (base × height) ÷ 2 = (6 × 8) ÷ 2 = 48 ÷ 2 = 24 m²
- White space = total − black = 96 − 24 = 72 m²

✔ Check: Triangle fits inside rectangle, base centered, height full — correct.

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Problem 2 (second one — also labeled “2”, but third figure):
This is a rectangle (8 m wide × 6 m tall) with a black triangle on the left and a white triangle on the right.

Wait — let’s read carefully:
- Rectangle: width = 8 m (horizontal), height = 6 m (vertical)
- Left side: black triangle with base = 5 m (horizontal), height = 6 m (vertical — same as rectangle height)
- Right side: white triangle with base = 6 m (horizontal), height = 6 m (vertical — same as rectangle height)

But note: The rectangle is only 8 m wide. If left triangle uses 5 m and right triangle uses 6 m, that’s 11 m total — too much! So likely the triangles are *inside* the rectangle, and the white space includes:
- The rectangle minus the black triangle,
- Plus the white triangle on the right? Wait — no, looking again: the figure shows the rectangle with a black triangle on the left, and then *outside* the rectangle, on the right, a white triangle attached (like in problem 1).

Yes — similar to problem 1: rectangle (8 m × 6 m), black triangle inside on left (base 5 m, height 6 m), and a white triangle attached on the right (base = 6 m, height = 6 m — because the vertical dashed line shows height = 6 m).

So white space =
- White part of rectangle = rectangle area − black triangle area
- Plus the external white triangle

Compute:

- Rectangle area = 8 × 6 = 48 m²
- Black triangle area = (5 × 6) ÷ 2 = 30 ÷ 2 = 15 m²
- White part of rectangle = 48 − 15 = 33 m²
- External white triangle = (6 × 6) ÷ 2 = 36 ÷ 2 = 18 m²
- Total white space = 33 + 18 = 51 m²

✔ Check dimensions: rectangle 8 m wide; black triangle takes 5 m of that width, leaving 3 m of white rectangle on the right *inside* the rectangle. Then an extra triangle sticks out beyond the rectangle — its base is 6 m, drawn from the right side, so it's external. That matches the diagram.

So final answers:
1. 75 m²
2. 72 m²
3. 51 m²

Final Answer:
75 m², 72 m², 51 m²