SME
Grade 6 Math · Problem type
Area of composite figures
Use this for the area of a house shape: a rectangle with a triangle on top.
Diagram
Area: 33 m².
The rectangle and the triangle roof add up to the whole shape.
This is an example. Type your own values to start a new problem.
S (m²)
=
w
×
H
+
½
×
w
×
r
R
Rectangle area
worked out (not typed)
T
Triangle area
worked out (not typed)
Formulas
w
×
H
=
R
(width
×
wall
height
=
rectangle
area)
6 × 4 = 24
1
2
×
w
×
r
=
T
(half
of
width
×
roof
height
=
triangle
area)
1
2
×
6
×
3
=
9
R
+
T
=
S
(rectangle
area
+
triangle
area
=
total
area)
24 + 9 = 33
Assumptions
•
Split the shape into a rectangle and a triangle, find each area, then add.
•
The triangle’s base is the rectangle’s width.
•
Lengths in meters to 20, areas in square meters.
Step-by-step
WE KNOW
w = 6 m (width), H = 4 m (wall height), r = 3 m (roof height)
FIND
rectangle area (R), triangle area (T), total area (S)
Step 1 · Find rectangle area (R)
Use w × H = R (width × wall height = rectangle area)
The walls are a rectangle: width times height.
R
=
6
×
4
R
=
24
m²
Step 2 · Find triangle area (T)
Use ½ × w × r = T (half of width × roof height = triangle area)
The roof is a triangle on the same width: half of base × height.
T
=
1
2
×
6
×
3
T
=
3
×
3
T
=
9
m²
Step 3 · Find total area (S)
Use R + T = S (rectangle area + triangle area = total area)
Add the two areas.
S
=
24
+
9
S
=
33
m²
Check
Put the numbers back in. Both sides should match.
6 × 4 = 24 ✓
1
2
×
6
×
3
=
9
✓
24 + 9 = 33 ✓
Topic check
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