SME
Grade 10 Math · Problem type
Trapezoid midsegment and area
Use this for “A trapezoid has bases 9 and 15 and height 5. Find its midsegment and area.”
Diagram
A trapezoid: one pair of parallel sides, AB and DC.
The dashed line is the height: the distance between the bases, at right angles.
This is an example. Type your own values to start a new problem.
K
=
+
2
×
h
m
Midsegment
worked out (not typed)
Formulas
m
=
b₁
+
b₂
2
12
=
15 + 9
2
K
=
m
×
h
60 = 12 × 5
Assumptions
•
A trapezoid has exactly one pair of parallel sides, the bases.
•
The midsegment joins the midpoints of the legs: it is parallel to the bases and their mean.
•
The area is the midsegment times the height.
•
Lengths are in any one unit.
Step-by-step
WE KNOW
b₁ = 15, b₂ = 9, h = 5
FIND
midsegment (m), area (K)
Step 1 · Find midsegment (m)
Use m = (b₁ + b₂) ÷ 2
The midsegment is the mean of the bases.
m
=
15 + 9
2
m
=
24
2
m
=
12
Step 2 · Find area (K)
Use K = m × h
The midsegment times the height.
K
=
12
×
5
K
=
60
Check
Put the numbers back in. Both sides should match.
12
=
15 + 9
2
✓
60 = 12 × 5 ✓
Topic check
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