Let’s solve this step by step.
We are given three polygons on a coordinate plane:
1. A green square (top left)
2. A blue rectangle (middle right)
3. A yellow triangle (bottom left)
We need to find the
area of each polygon using their coordinates.
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Step 1: Green Square
Look at the red dots — they mark the corners.
From the grid:
- Bottom-left corner: (-7, -1)
- Bottom-right corner: (-2, -1)
- Top-right corner: (-2, 4)
- Top-left corner: (-7, 4)
To find side length:
Horizontal side: from x = -7 to x = -2 → that’s 5 units.
Vertical side: from y = -1 to y = 4 → also 5 units.
So it’s a square with side = 5.
Area of square = side × side = 5 × 5 =
25
✔ Check: Count squares on grid — yes, 5 across and 5 down → 25 small squares.
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Step 2: Blue Rectangle
Black dots mark the corners.
From grid:
- Bottom-left: (4, -4)
- Bottom-right: (6, -4)
- Top-right: (6, 3)
- Top-left: (4, 3)
Width (horizontal): from x=4 to x=6 → 2 units
Height (vertical): from y=-4 to y=3 → 7 units
Area of rectangle = width × height = 2 × 7 =
14
✔ Check: Count columns (2) and rows (7) → 2×7=14.
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Step 3: Yellow Triangle
Orange dots mark the corners.
From grid:
- Left bottom: (-9, -10)
- Right bottom: (-1, -10)
- Top point: (-5, -5)
Base: from x=-9 to x=-1 → that’s 8 units long (since -1 - (-9) = 8)
Height: from base at y=-10 up to top at y=-5 → that’s 5 units high (since -5 - (-10) = 5)
Area of triangle = (base × height) ÷ 2 = (8 × 5) ÷ 2 = 40 ÷ 2 =
20
✔ Check: You can imagine fitting this triangle inside a rectangle 8 wide and 5 tall — triangle is half of that → 20.
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Now let’s add them all together if needed? Wait — the problem doesn’t say “total area”. It just shows the polygons. But since no specific question is asked in the image, and the user said “solve the problem”, we assume they want the area of each shape.
But looking again — maybe the task is implied to find areas? Since it’s Grade 6 and standards 6.NS.8 and 6.G.3 relate to plotting points and finding area on coordinate plane.
Since no explicit question is written, but the title is “Polygons in the Coordinate Plane”, and shapes are drawn, the most logical task is to
find the area of each polygon.
So final answers per shape:
Green square: 25
Blue rectangle: 14
Yellow triangle: 20
If the problem expects total area, then 25 + 14 + 20 = 59 — but unless specified, better to list each.
Wait — perhaps the original problem (not shown fully) asks for something else? But based on what’s visible, and common textbook problems, finding individual areas is standard.
Alternatively, maybe the student is supposed to identify vertices or something — but again, without explicit instructions, area is the most meaningful calculation here.
Given that, I’ll provide the area of each.
Final Answer:
Green square: 25
Blue rectangle: 14
Yellow triangle: 20
Parent Tip: Review the logic above to help your child master the concept of polygons in the coordinate plane worksheet.
