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A parallelogram-shaped kite has one side 20 cm with a matching height of 9 cm. Its adjacent side measures 15 cm. What height goes with the 15 cm side (in cm)?

Class 7Perimeter and AreaPerimeter and Area
  • A9
  • B6.75
  • C180
  • D12

Step-by-Step Solution

The area is the same whichever side you call the base. Area = . With the 15 cm side as base: → cm. Reusing the 9 cm height with the wrong side is the classic slip; 180 is the area, not a height.
Answer: D) 12

Key idea: Parallelogram area

**Area of a parallelogram = base × height.**

Same idea as a rectangle, but the height is the perpendicular distance between the two parallel sides — NOT the slant length of the side. Pick any side as the base, drop a perpendicular to the opposite parallel side, measure that — that's the height.

Example: parallelogram with base 8 cm and perpendicular height 5 cm. Area = . The slant side could be longer; doesn't matter for area.

Perimeter of a parallelogram = 2 × (one side + adjacent side).

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