Question

area and perimeter of shapes on the coordinate plane
directions:
on the coordinate plane
✅ plot the ordered pairs to create shapes in each quadrant.
✅ label the shape you created.
✅ find the area of each shape
✅ find the perimeter of each shape
✅ color in each shape
quadrant i
a (2,1), b (5,1), c (2,4), d (5,4)
shape:
area: _______ perimeter: _______
quadrant ii
a (-5,5), b (-1,5), c (-5,3), d (-1,3)
shape:
area: _______ perimeter: _______
quadrant iii
a (-5,-1) b (-1,-1) c (-5,-3) d (-1,-3)
shape:
area: _______ perimeter: _______
quadrant iv (compound shape)
a(1,-1), b (4,-1), c (1,-4), d (6,-4), e(6,-3),f(4,-3)
shape:
area: _______ perimeter: _______

Explanation:

Step1: Plot Quadrant I points

Plot $A(2,1)$, $B(5,1)$, $C(2,4)$, $D(5,4)$; connect to form a rectangle.

Step2: Calculate Quadrant I area

Area = length × width = $(5-2) \times (4-1) = 3 \times 3 = 9$

Step3: Calculate Quadrant I perimeter

Perimeter = $2 \times (length + width) = 2 \times (3+3) = 12$

Step4: Plot Quadrant II points

Plot $A(-5,5)$, $B(-1,5)$, $C(-5,3)$, $D(-1,3)$; connect to form a rectangle.

Step5: Calculate Quadrant II area

Area = $(-1 - (-5)) \times (5-3) = 4 \times 2 = 8$

Step6: Calculate Quadrant II perimeter

Perimeter = $2 \times (4+2) = 12$

Step7: Plot Quadrant III points

Plot $A(-5,-1)$, $B(-1,-1)$, $C(-5,-3)$, $D(-1,-3)$; connect to form a rectangle.

Step8: Calculate Quadrant III area

Area = $(-1 - (-5)) \times (-1 - (-3)) = 4 \times 2 = 8$

Step9: Calculate Quadrant III perimeter

Perimeter = $2 \times (4+2) = 12$

Step10: Plot Quadrant IV points

Plot $A(1,-1)$, $B(4,-1)$, $C(1,-4)$, $D(6,-4)$, $E(6,-3)$, $F(4,-3)$; split into 2 rectangles: $A-B-F-E$ and $E-D-C-A$

Step11: Calculate Quadrant IV area

Area = $(4-1) \times (-1 - (-3)) + (6-1) \times (-3 - (-4)) = 3 \times 2 + 5 \times 1 = 6 + 5 = 11$

Step12: Calculate Quadrant IV perimeter

Sum side lengths: $3 + 2 + 2 + 1 + 5 + 1 + 3 + 2 = 19$

Answer:

Quadrant I

Shape: Rectangle
Area: $9$
Perimeter: $12$

Quadrant II

Shape: Rectangle
Area: $8$
Perimeter: $12$

Quadrant III

Shape: Rectangle
Area: $8$
Perimeter: $12$

Quadrant IV

Shape: Irregular Compound Shape
Area: $11$
Perimeter: $19$