Step 1 of 10
Start
Treat the whole shape like an area ledger.
Survey 1170829
parallelogram base 20 cm · triangle base 8 cm · triangle area 28 cm²
trapezoid = parallelogram 135 cm² + triangle · parallel sides 15 cm and 20 cm
parallelogram area 960 m² · triangle base 24 m · triangle height 10 m
Read
whole
whole
Share
height
height
Value
pieces
pieces
Add or
subtract
subtract
Reconcile
ledger
ledger
Composite survey desk
One whole, two non-overlapping pieces
The cut does not change the area. It only names a triangle and a trapezoid inside the parallelogram.
× 2, then ÷ 8 to undo ½ × 8
Recover height
½ × 8 × h = 28
h = (2 × 28) ÷ 8 = 7 cm
h = (2 × 28) ÷ 8 = 7 cm
Value the whole
20 × 7 = 140 cm²
× base × the same perpendicular height
Area ledgercm²
whole parallelogram140
known triangle− 28
missing trapezoid112 cm²
− remove the known piece once
28
112
Now the parallelogram is the known piece
The same ledger works in reverse: value the extra triangle, then add it to the parallelogram.
÷ 15 to recover h
Shared height
135 ÷ 15 = 9 cm
− 15 from the whole base
Extra triangle base
20 − 15 = 5 cm
÷ 2 because the extra piece is a triangle
Extra triangle
½ × 5 × 9 = 22.5 cm²
+ join the two non-overlapping pieces
Area ledgercm²
parallelogram135
extra triangle+ 22.5
whole trapezoid157.5 cm²
Balance this field ledger
Find the triangle first. Then subtract it from the whole parallelogram to find the trapezoid.
Both pieces must add back to 960 m².
Show both component areas on your whiteboard.
Write the triangle calculation, subtract it from 960 m², and check that the two pieces reconcile. Submit your work to unlock the receipt.
Work submitted. The area receipt is unlocked.
The field ledger reconciles exactly
Every square metre belongs to one piece—none is lost and none is counted twice.
÷ 2 because the first piece is a triangle
Area survey · 1272076
½ × 24 × 10120 m²
− remove the known triangle once
960 − 120840 m²
120 + 840960 m² ✓
120
840
shared height used10 m
pieces overlapno
ledger difference0 m²
0 Δ
Area ledger balanced.
The shared height connects the shapes. Value each non-overlapping piece, then add or subtract exactly once until the pieces match the whole.
1share height
2value pieces
3reconcile whole