Identify and Calculate the Area and Perimeter for Each ... - Free Printable

To solve the problem of identifying and calculating the area and perimeter for each quadrilateral, we need to follow these steps:

1. Identify the type of quadrilateral (e.g., rectangle, square, parallelogram).
2. Use the appropriate formulas for area and perimeter based on the type of quadrilateral.
3. Substitute the given values into the formulas.
4. Perform the calculations to find the area and perimeter.

Let's go through each quadrilateral step by step.

---

1) Rectangle

- Given: \( a = 77 \, \text{yds} \), \( b = 45 \, \text{yds} \)
- Type: Rectangle
- Formulas:
- Area: \( \text{Area} = a \times b \)
- Perimeter: \( \text{Perimeter} = 2(a + b) \)

#### Calculations:
- Area:
\[
\text{Area} = 77 \times 45 = 3465 \, \text{square yards}
\]

- Perimeter:
\[
\text{Perimeter} = 2(77 + 45) = 2 \times 122 = 244 \, \text{yards}
\]

#### Final Answer:
\[
\boxed{\text{Area: } 3465 \, \text{square yards}, \, \text{Perimeter: } 244 \, \text{yards}}
\]

---

2) Rectangle

- Given: \( a = 68 \, \text{cm} \), \( b = 46 \, \text{cm} \)
- Type: Rectangle
- Formulas:
- Area: \( \text{Area} = a \times b \)
- Perimeter: \( \text{Perimeter} = 2(a + b) \)

#### Calculations:
- Area:
\[
\text{Area} = 68 \times 46 = 3128 \, \text{square cm}
\]

- Perimeter:
\[
\text{Perimeter} = 2(68 + 46) = 2 \times 114 = 228 \, \text{cm}
\]

#### Final Answer:
\[
\boxed{\text{Area: } 3128 \, \text{square cm}, \, \text{Perimeter: } 228 \, \text{cm}}
\]

---

3) Square

- Given: \( s = 52 \, \text{inches} \)
- Type: Square
- Formulas:
- Area: \( \text{Area} = s^2 \)
- Perimeter: \( \text{Perimeter} = 4s \)

#### Calculations:
- Area:
\[
\text{Area} = 52^2 = 2704 \, \text{square inches}
\]

- Perimeter:
\[
\text{Perimeter} = 4 \times 52 = 208 \, \text{inches}
\]

#### Final Answer:
\[
\boxed{\text{Area: } 2704 \, \text{square inches}, \, \text{Perimeter: } 208 \, \text{inches}}
\]

---

4) Square

- Given: \( s = 51 \, \text{ft} \)
- Type: Square
- Formulas:
- Area: \( \text{Area} = s^2 \)
- Perimeter: \( \text{Perimeter} = 4s \)

#### Calculations:
- Area:
\[
\text{Area} = 51^2 = 2601 \, \text{square feet}
\]

- Perimeter:
\[
\text{Perimeter} = 4 \times 51 = 204 \, \text{feet}
\]

#### Final Answer:
\[
\boxed{\text{Area: } 2601 \, \text{square feet}, \, \text{Perimeter: } 204 \, \text{feet}}
\]

---

5) Rectangle

- Given: \( a = 58 \, \text{ft} \), \( b = 39 \, \text{ft} \)
- Type: Rectangle
- Formulas:
- Area: \( \text{Area} = a \times b \)
- Perimeter: \( \text{Perimeter} = 2(a + b) \)

#### Calculations:
- Area:
\[
\text{Area} = 58 \times 39 = 2262 \, \text{square feet}
\]

- Perimeter:
\[
\text{Perimeter} = 2(58 + 39) = 2 \times 97 = 194 \, \text{feet}
\]

#### Final Answer:
\[
\boxed{\text{Area: } 2262 \, \text{square feet}, \, \text{Perimeter: } 194 \, \text{feet}}
\]

---

6) Parallelogram

- Given: \( a = 81 \, \text{mm} \), \( b = 64 \, \text{mm} \), \( h = 52 \, \text{mm} \)
- Type: Parallelogram
- Formulas:
- Area: \( \text{Area} = b \times h \) (base times height)
- Perimeter: \( \text{Perimeter} = 2(a + b) \)

#### Calculations:
- Area:
\[
\text{Area} = 64 \times 52 = 3328 \, \text{square mm}
\]

- Perimeter:
\[
\text{Perimeter} = 2(81 + 64) = 2 \times 145 = 290 \, \text{mm}
\]

#### Final Answer:
\[
\boxed{\text{Area: } 3328 \, \text{square mm}, \, \text{Perimeter: } 290 \, \text{mm}}
\]

---

7) Triangle (Note: This is not a quadrilateral, so it is excluded from the task.)

---

8) Trapezoid

- Given: \( a = 40.19 \, \text{cm} \), \( b = 61 \, \text{cm} \), \( h = 47 \, \text{cm} \)
- Type: Trapezoid
- Formulas:
- Area: \( \text{Area} = \frac{1}{2}(a + b) \times h \)
- Perimeter: \( \text{Perimeter} = a + b + c + d \) (where \( c \) and \( d \) are the non-parallel sides; not given here)

#### Calculations:
- Area:
\[
\text{Area} = \frac{1}{2}(40.19 + 61) \times 47 = \frac{1}{2}(101.19) \times 47 = 50.595 \times 47 = 2377.965 \, \text{square cm}
\]

- Perimeter: Since the non-parallel sides are not given, we cannot calculate the perimeter.

#### Final Answer:
\[
\boxed{\text{Area: } 2377.965 \, \text{square cm}, \, \text{Perimeter: } \text{Not calculable}}
\]

---

9) Trapezoid

- Given: \( a = 94 \, \text{cm} \), \( b = 71.15 \, \text{cm} \), \( h = 7 \, \text{cm} \)
- Type: Trapezoid
- Formulas:
- Area: \( \text{Area} = \frac{1}{2}(a + b) \times h \)
- Perimeter: \( \text{Perimeter} = a + b + c + d \) (where \( c \) and \( d \) are the non-parallel sides; not given here)

#### Calculations:
- Area:
\[
\text{Area} = \frac{1}{2}(94 + 71.15) \times 7 = \frac{1}{2}(165.15) \times 7 = 82.575 \times 7 = 578.025 \, \text{square cm}
\]

- Perimeter: Since the non-parallel sides are not given, we cannot calculate the perimeter.

#### Final Answer:
\[
\boxed{\text{Area: } 578.025 \, \text{square cm}, \, \text{Perimeter: } \text{Not calculable}}
\]

---

10) Rhombus

- Given: \( a = 93 \, \text{m} \), \( b = 93 \, \text{m} \), \( h = 82 \, \text{m} \)
- Type: Rhombus
- Formulas:
- Area: \( \text{Area} = b \times h \) (base times height)
- Perimeter: \( \text{Perimeter} = 4a \)

#### Calculations:
- Area:
\[
\text{Area} = 93 \times 82 = 7626 \, \text{square meters}
\]

- Perimeter:
\[
\text{Perimeter} = 4 \times 93 = 372 \, \text{meters}
\]

#### Final Answer:
\[
\boxed{\text{Area: } 7626 \, \text{square meters}, \, \text{Perimeter: } 372 \, \text{meters}}
\]

---

Final Summary of Answers

1. Rectangle: \( \text{Area: } 3465 \, \text{square yds}, \, \text{Perimeter: } 244 \, \text{yds} \)
2. Rectangle: \( \text{Area: } 3128 \, \text{square cm}, \, \text{Perimeter: } 228 \, \text{cm} \)
3. Square: \( \text{Area: } 2704 \, \text{square in}, \, \text{Perimeter: } 208 \, \text{in} \)
4. Square: \( \text{Area: } 2601 \, \text{square ft}, \, \text{Perimeter: } 204 \, \text{ft} \)
5. Rectangle: \( \text{Area: } 2262 \, \text{square ft}, \, \text{Perimeter: } 194 \, \text{ft} \)
6. Parallelogram: \( \text{Area: } 3328 \, \text{square mm}, \, \text{Perimeter: } 290 \, \text{mm} \)
7. Triangle: Excluded (not a quadrilateral)
8. Trapezoid: \( \text{Area: } 2377.965 \, \text{square cm}, \, \text{Perimeter: } \text{Not calculable} \)
9. Trapezoid: \( \text{Area: } 578.025 \, \text{square cm}, \, \text{Perimeter: } \text{Not calculable} \)
10. Rhombus: \( \text{Area: } 7626 \, \text{square m}, \, \text{Perimeter: } 372 \, \text{m} \)

\boxed{\text{All answers calculated as shown above.}}