5 a) Write the formula for the area (A) of a parallelogram in terms of its

base (b) and its perpendicular height (h).

b) A parallelogram has an area of 714 cm2

and a base of 42 cm.

Form and solve an equation to find the height (h) of this

parallelogram.

h = cm

c) A parallelogram with a perpendicular height of 4.7 cm has an area

of 29.61 cm2

Form and solve an equation to find the length of the base (b) of

this parallelogram.

b = cm

6 Here is a pentagon.

a) Write a formula for the perimeter (P) in terms of x and y.

P =

The perimeter of the pentagon is 79 cm.

b) If y = 17 cm, form and solve an equation to find the value of x.

x = cm

c) If x = 17 cm, form and solve an equation to find the value of y.

y = cm

### 5. a) Formula for the area of a parallelogram:
The area \(A\) of a parallelogram is given by:
\[
A = b \times h
\]
where:
- \(A\) is the area,
- \(b\) is the base, and
- \(h\) is the perpendicular height.

### 5. b) Finding the height (\(h\)) of a parallelogram:
Given:
- Area \(A = 714 \, \text{cm}^2\),
- Base \(b = 42 \, \text{cm}\).

Using the formula for the area:
\[
A = b \times h
\]
Substitute the given values:
\[
714 = 42 \times h
\]
Solve for \(h\):
\[
h = \frac{714}{42} = 17 \, \text{cm}
\]

### 5. c) Finding the base (\(b\)) of a parallelogram:
Given:
- Area \(A = 29.61 \, \text{cm}^2\),
- Height \(h = 4.7 \, \text{cm}\).

Using the formula for the area:
\[
A = b \times h
\]
Substitute the given values:
\[
29.61 = b \times 4.7
\]
Solve for \(b\):
\[
b = \frac{29.61}{4.7} = 6.3 \, \text{cm}
\]

---

### 6. a) Formula for the perimeter of a pentagon:
Assuming the pentagon has sides of lengths \(x\) and \(y\), and that three sides are \(x\) and two sides are \(y\), the formula for the perimeter \(P\) is:
\[
P = 3x + 2y
\]

### 6. b) Finding \(x\) when \(y = 17 \, \text{cm}\) and \(P = 79 \, \text{cm}\):
Substitute into the perimeter formula:
\[
79 = 3x + 2(17)
\]
Simplify:
\[
79 = 3x + 34
\]
Solve for \(x\):
\[
3x = 79 - 34 = 45
\]
\[
x = \frac{45}{3} = 15 \, \text{cm}
\]

### 6. c) Finding \(y\) when \(x = 17 \, \text{cm}\) and \(P = 79 \, \text{cm}\):
Substitute into the perimeter formula:
\[
79 = 3(17) + 2y
\]
Simplify:
\[
79 = 51 + 2y
\]
Solve for \(y\):
\[
2y = 79 - 51 = 28
\]
\[
y = \frac{28}{2} = 14 \, \text{cm}
\]

---

### Would you like more details or have any questions?

#### Related questions:
1. What is the formula for the area of a parallelogram with given sides and angles?
2. How does the formula for the area of a parallelogram relate to that of a triangle?
3. What would happen to the area if the base or height of the parallelogram doubles?
4. How do you find the perimeter of a pentagon if all sides are equal?
5. Can you find the area of an irregular pentagon?

**Tip**: For solving area problems, always ensure that the height is perpendicular to the base.

5 a) Write the formula for the area (A) of a parallelogram in terms of its base (b) and its perpendicular height (h).

b) A parallelogram has an area of 714 cm² and a base of 42 cm. Form and solve an equation to find the height (h) of this parallelogram.

h = cm

c) A parallelogram with a perpendicular height of 4.7 cm has an area of 29.61 cm². Form and solve an equation to find the length of the base (b) of this parallelogram.

b = cm

6 Here is a pentagon.

a) Write a formula for the perimeter (P) in terms of x and y.

P =

The perimeter of the pentagon is 79 cm.

b) If y = 17 cm, form and solve an equation to find the value of x.

x = cm

c) If x = 17 cm, form and solve an equation to find the value of y.

y = cm

Learn how to calculate the area of a parallelogram using base and height, and how to solve for unknown dimensions. Also, explore how to find the perimeter of a pentagon with mixed side lengths. Detailed step-by-step solutions for students in Grades 6-8.

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