SME
Grade 6 Math · Problem type
Area of trapezoids
Use this for “The bases are 9 and 15, the height 8. Find the area.”
Diagram
Area: 30 cm².
Leaning the shape keeps the base, the height and the area.
This is an example. Type your own values to start a new problem.
A (cm²)
=
½
×
b₁
×
h
+
½
×
b₂
×
h
Formulas
A
=
1
2
×
b₁
×
h
+
1
2
×
b₂
×
h
(area
=
one
triangle
+
the
other
triangle)
30
=
1
2
×
4
×
5
+
1
2
×
8
×
5
Assumptions
•
A diagonal cuts the trapezoid into two triangles with the same height.
•
One triangle has the bottom base, the other the top base.
•
The two bases are the parallel sides. It is the same area as ½ × (b₁ + b₂) × h.
Step-by-step
WE KNOW
b₁ = 4 cm (bottom base), b₂ = 8 cm (top base), h = 5 cm (height)
FIND
area (A)
Step 1 · Find area (A)
Use A = ½ × b₁ × h + ½ × b₂ × h (area = one triangle + the other triangle)
Find each triangle’s area, then add them.
A
=
1
2
×
4
×
5
+
1
2
×
8
×
5
1
2
×
4
×
5
=
10
1
2
×
8
×
5
=
20
10 + 20 = 30
A
=
30
cm²
Check
Put the numbers back in. Both sides should match.
30
=
1
2
×
4
×
5
+
1
2
×
8
×
5
✓
Topic check
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Related lessons
Area of triangles, parallelograms and trapezoids
Main lesson
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Use this for “A triangle has base 3 and height 7. What is its area?”
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Which segment is a height?
Use this for “Which segment is a height for this base?”