Let’s solve each problem step by step.
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Problem 4: Parallelogram
We are given a parallelogram on grid paper. To find its area, we use:
>
Area = base × height
Look at the shape:
- The
base (B) is the bottom side — count how many squares long it is horizontally.
→ From left to right along the bottom: it spans
5 units.
- The
height (h) is the vertical distance from the base to the top side (not slanted!).
→ Count straight up from the base to the top: that’s
3 units.
So:
> Area = 5 × 3 =
15 square units
✔ Check: Yes, in a parallelogram, height must be perpendicular to the base — and here, since it's drawn on grid lines, counting vertically gives us the correct height.
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Problem 5: L-shaped figure
This is not a standard shape, so we break it into rectangles.
Option 1: Split into two rectangles.
- Left rectangle: width = 4, height = 5 → area = 20
- Bottom-right rectangle: width = 4, height = 2 → area = 8
Wait — let me check coordinates or grid counts carefully.
Actually, looking again:
The full shape can also be seen as:
- A big rectangle of 8 units wide and 5 units tall? No — because part is missing.
Better way: split vertically.
Left part: 4 units wide × 5 units high = 20
Right part: only the bottom part — from x=4 to x=8 (so 4 units wide), but only y=0 to y=2 (so 2 units high) → 4×2 = 8
Total = 20 + 8 =
28
Alternatively, think of it as a large rectangle minus a missing piece.
Large rectangle if complete: 8 wide × 5 high = 40
Missing piece: top right — from x=4 to x=8 (4 units), y=2 to y=5 (3 units) → 4×3 = 12
Then area = 40 - 12 =
28
Same answer.
✔ So Area =
28 square units
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Problem 16: Triangle
Formula for triangle area:
>
Area = ½ × base × height
On the grid:
- Base (B): horizontal side at bottom — count squares →
6 units
- Height (h): vertical distance from base to opposite vertex →
4 units
So:
> Area = ½ × 6 × 4 = 3 × 4 =
12 square units
✔ Correct — right triangle, legs are base and height.
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Problem 17: Trapezoid
Formula:
>
Area = ½ × height × (base₁ + base₂)
Identify:
- Base₁ (bottom base): longer parallel side → count squares →
8 units
- Base₂ (top base): shorter parallel side →
4 units
- Height (h): vertical distance between the two bases →
4 units
Plug in:
> Area = ½ × 4 × (8 + 4) = 2 × 12 =
24 square units
✔ Double-check: yes, trapezoid has two parallel sides; height is perpendicular distance between them — which is 4 units here.
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Final Answer:
4. B = 5, h = 3, Area = 15 square units
5. Area = 28 square units
16. B = 6, h = 4, Area = 12 square units
17. B₁ = 8, b₂ = 4, h = 4, Area = 24 square units
Parent Tip: Review the logic above to help your child master the concept of polygons in the coordinate plane worksheet.
