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💡 What Is a Parallelogram?
A parallelogram is a 4-sided shape where opposite sides are parallel and equal. A rectangle is a special parallelogram with right angles — but most parallelograms lean to the side.
We pick one side as the base (b). The height (h) is the perpendicular distance from the base to the opposite side — straight up, not along the slanted side!
Rectangle vs. Parallelogram
The blue dashed line is the height — always perpendicular to the base, never the red slanted side!
⭐ Quick Check
A rectangle and a square are both special parallelograms — when every angle is a right angle, the height is simply the side length, so no perpendicular guesswork is needed. But for a leaning parallelogram, always measure straight up from the base to find h, not along the slanted side.
⚠️ Watch out: If a problem also tells you the length of the slanted side, don't use it for the area! Only the perpendicular height belongs in the formula.
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✂️ Cut and Slide → Rectangle!
Cut a triangle off one side of the parallelogram, slide it to the other side, and you get a rectangle with the same base and height!
So the parallelogram has the same area as a rectangle with length b and width h.
The Cut-and-Slide Trick
Same base, same height, same area — it's just rearranged! That's why area = b × h.
Area of a parallelogram
Area = base × height = b × h
Worked Example
Find the area of a parallelogram with base 9 cm and height 5 cm:
Step 1: Write the formula → Area = b × h
Step 2: Plug in → 9 × 5
Step 3: Calculate → 45 cm² ✓
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1 Use the Formula 📐
Find the area using Area = b × h.
b = 6 cm, h = 4 cm
Area = 6 × 4 = cm²
b = 8 m, h = 3 m
Area = × = m²
b = 10 cm, h = 7 cm
Area = cm²
b = 12 m, h = 9 m
Area = m²
2 Spot the Trick 🕵️
Each problem gives extra information. Pick the right base and height!
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A parallelogram has base 10 cm, height 6 cm, and slanted side 7 cm.
Area = cm² (don't use the 7!)
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A parallelogram has base 12 m, height 5 m, and slanted side 8 m.
Area = m²
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A parallelogram has base 15 cm, slanted side 10 cm, and height 4 cm.
Area = cm²
3 Find the Missing Number 🔍
Area = b × h, so b = Area ÷ h and h = Area ÷ b.
Area = 40 cm², b = 8 cm → h = cm
Area = 54 m², h = 6 m → b = m
Area = 63 cm², b = 9 cm → h = cm
Area = 32 m², h = 4 m → b = m
Answer Key:
1) 24; 8×3=24; 70; 108 —
2) 60 cm²; 60 m²; 60 cm² —
3) 5, 9, 7, 8