SME
Grade 6 Math · Problem type
Polygons on the coordinate plane
Use this for “A rectangle has corners at (−2, 3) and (5, −2). Find its area.”
Chart
A rectangle 7 units wide and 5 units tall.
This is an example. Type your own values to start a new problem.
Left x-coordinate
example
Right x-coordinate
example
Bottom y-coordinate
example
Top y-coordinate
example
Width
calculated · units
Height
calculated · units
Area
worked out (not typed) · square units
Perimeter
worked out (not typed) · units
Formulas
From −3 across to 4: 7
From the left x-coordinate across to the right one = width
From −2 up to 3: 5
From the bottom y-coordinate up to the top one = height
7 × 5 = 35
Width × height = area
2 × (7 + 5) = 24
2 × (width + height) = perimeter
Assumptions
•
The sides run along the grid, so each side is a distance on one row or one column.
•
Area = width × height; perimeter = 2 × (width + height).
•
Coordinates from −10,000 to 10,000; lengths in units, area in square units.
Step-by-step
WE KNOW
Left x-coordinate: −3
Right x-coordinate: 4
Bottom y-coordinate: −2
Top y-coordinate: 3
FIND
width, height, area, perimeter
Step 1 · Find width
From −3 across to 4: ?
From the left x-coordinate across to the right one = width
The width is the distance along a row from the left side to the right side.
−3 and 4 are on opposite sides of 0: add their distances from 0.
|−3| + |4| = 3 + 4 = 7
Width = 7 units
Step 2 · Find height
From −2 up to 3: ?
From the bottom y-coordinate up to the top one = height
The height is the distance along a column from the bottom up to the top.
−2 and 3 are on opposite sides of 0: add their distances from 0.
|−2| + |3| = 2 + 3 = 5
Height = 5 units
Step 3 · Find area
7 × 5 = ?
Width × height = area
Multiply the width by the height.
Area = 35 square units
Step 4 · Find perimeter
2 × (7 + 5) = ?
2 × (width + height) = perimeter
Add the width and height, then double: two of each side.
Perimeter = 24 units
Check
Put the numbers back in. Both sides should match.
|−3| + |4| = 3 + 4 = 7 ✓
|−2| + |3| = 2 + 3 = 5 ✓
7 × 5 = 35 ✓
2 × (7 + 5) = 24 ✓
Topic check
See what you know: 5 questions on this topic
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