6.G.A.3 Worksheets - Common Core Math - Free Printable
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Step-by-step solution for: 6.G.A.3 Worksheets - Common Core Math
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Show Answer Key & Explanations
Step-by-step solution for: 6.G.A.3 Worksheets - Common Core Math
Here are the step-by-step solutions to find the area for each shape on the coordinate plane.
To solve these, we look at the coordinates to find the base (width) and height of each shape. Then we use the formula: $\text{Area} = \text{base} \times \text{height}$.
* Vertices: $A(7, 6)$, $B(7, -5)$, $C(5, -5)$, $D(5, 6)$
* Find the Height: Look at the y-coordinates (up and down). The shape goes from $y = 6$ down to $y = -5$.
* Distance = $6 - (-5) = 11$ units.
* Find the Base: Look at the x-coordinates (left and right). The shape goes from $x = 5$ to $x = 7$.
* Distance = $7 - 5 = 2$ units.
* Calculate Area: $11 \times 2 = 22$.
Area = 22 square units
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* Vertices: $E(-4, 5)$, $F(2, 5)$, $G(2, -5)$, $H(-4, -5)$
* Find the Base: Look at the x-coordinates. From $x = -4$ to $x = 2$.
* Distance = $2 - (-4) = 6$ units.
* Find the Height: Look at the y-coordinates. From $y = 5$ down to $y = -5$.
* Distance = $5 - (-5) = 10$ units.
* Calculate Area: $6 \times 10 = 60$.
Area = 60 square units
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* Vertices: $J(-8, -2)$, $K(-5, -2)$, $L(-8, -8)$ *(Note: The fourth point is likely $(-5, -8)$ to make a rectangle)*
* Find the Base: Look at the x-coordinates. From $x = -8$ to $x = -5$.
* Distance = $-5 - (-8) = 3$ units.
* Find the Height: Look at the y-coordinates. From $y = -2$ down to $y = -8$.
* Distance = $-2 - (-8) = 6$ units.
* Calculate Area: $3 \times 6 = 18$.
Area = 18 square units
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* Vertices: $M(8, 9)$, $N(1, 9)$, $O(1, 5)$, $P(8, 5)$
* Find the Base: Look at the x-coordinates. From $x = 1$ to $x = 8$.
* Distance = $8 - 1 = 7$ units.
* Find the Height: Look at the y-coordinates. From $y = 5$ up to $y = 9$.
* Distance = $9 - 5 = 4$ units.
* Calculate Area: $7 \times 4 = 28$.
Area = 28 square units
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* Vertices: $Q(0, 3)$, $R(0, 5)$, $S(2, 5)$, $T(?, ?)$
* Find the Side Length: Since it is a square, all sides are equal. Let's check the distance between $Q$ and $R$.
* Vertical side (y-coords): $5 - 3 = 2$ units.
* Horizontal side (x-coords from Q to T or R to S): $2 - 0 = 2$ units.
* Calculate Area: For a square, $\text{Area} = \text{side} \times \text{side}$.
* $2 \times 2 = 4$.
Area = 4 square units
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* Vertices: $W(-10, 5)$, $X(-8, 5)$, $Y(-8, -3)$, $Z(-10, -3)$
* Find the Base: Look at the x-coordinates. From $x = -10$ to $x = -8$.
* Distance = $-8 - (-10) = 2$ units.
* Find the Height: Look at the y-coordinates. From $y = 5$ down to $y = -3$.
* Distance = $5 - (-3) = 8$ units.
* Calculate Area: $2 \times 8 = 16$.
Area = 16 square units
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Final Answer:
ABCD Area: 22 square units
EFGH Area: 60 square units
JIKL Area: 18 square units
MNOP Area: 28 square units
QRST Area: 4 square units
WXYZ Area: 16 square units
To solve these, we look at the coordinates to find the base (width) and height of each shape. Then we use the formula: $\text{Area} = \text{base} \times \text{height}$.
1. Rectangle ABCD
* Vertices: $A(7, 6)$, $B(7, -5)$, $C(5, -5)$, $D(5, 6)$
* Find the Height: Look at the y-coordinates (up and down). The shape goes from $y = 6$ down to $y = -5$.
* Distance = $6 - (-5) = 11$ units.
* Find the Base: Look at the x-coordinates (left and right). The shape goes from $x = 5$ to $x = 7$.
* Distance = $7 - 5 = 2$ units.
* Calculate Area: $11 \times 2 = 22$.
Area = 22 square units
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2. Rectangle EFGH
* Vertices: $E(-4, 5)$, $F(2, 5)$, $G(2, -5)$, $H(-4, -5)$
* Find the Base: Look at the x-coordinates. From $x = -4$ to $x = 2$.
* Distance = $2 - (-4) = 6$ units.
* Find the Height: Look at the y-coordinates. From $y = 5$ down to $y = -5$.
* Distance = $5 - (-5) = 10$ units.
* Calculate Area: $6 \times 10 = 60$.
Area = 60 square units
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3. Rectangle JIKL
* Vertices: $J(-8, -2)$, $K(-5, -2)$, $L(-8, -8)$ *(Note: The fourth point is likely $(-5, -8)$ to make a rectangle)*
* Find the Base: Look at the x-coordinates. From $x = -8$ to $x = -5$.
* Distance = $-5 - (-8) = 3$ units.
* Find the Height: Look at the y-coordinates. From $y = -2$ down to $y = -8$.
* Distance = $-2 - (-8) = 6$ units.
* Calculate Area: $3 \times 6 = 18$.
Area = 18 square units
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4. Rectangle MNOP
* Vertices: $M(8, 9)$, $N(1, 9)$, $O(1, 5)$, $P(8, 5)$
* Find the Base: Look at the x-coordinates. From $x = 1$ to $x = 8$.
* Distance = $8 - 1 = 7$ units.
* Find the Height: Look at the y-coordinates. From $y = 5$ up to $y = 9$.
* Distance = $9 - 5 = 4$ units.
* Calculate Area: $7 \times 4 = 28$.
Area = 28 square units
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5. Square QRST
* Vertices: $Q(0, 3)$, $R(0, 5)$, $S(2, 5)$, $T(?, ?)$
* Find the Side Length: Since it is a square, all sides are equal. Let's check the distance between $Q$ and $R$.
* Vertical side (y-coords): $5 - 3 = 2$ units.
* Horizontal side (x-coords from Q to T or R to S): $2 - 0 = 2$ units.
* Calculate Area: For a square, $\text{Area} = \text{side} \times \text{side}$.
* $2 \times 2 = 4$.
Area = 4 square units
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6. Rectangle WXYZ
* Vertices: $W(-10, 5)$, $X(-8, 5)$, $Y(-8, -3)$, $Z(-10, -3)$
* Find the Base: Look at the x-coordinates. From $x = -10$ to $x = -8$.
* Distance = $-8 - (-10) = 2$ units.
* Find the Height: Look at the y-coordinates. From $y = 5$ down to $y = -3$.
* Distance = $5 - (-3) = 8$ units.
* Calculate Area: $2 \times 8 = 16$.
Area = 16 square units
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Final Answer:
ABCD Area: 22 square units
EFGH Area: 60 square units
JIKL Area: 18 square units
MNOP Area: 28 square units
QRST Area: 4 square units
WXYZ Area: 16 square units
Parent Tip: Review the logic above to help your child master the concept of 6 g 3 worksheet.
