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 $b$: $b = \frac{29.61}{4.7} = 6.3 \, \text{cm}$

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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 $y$: $2y = 79 - 51 = 28$ $y = \frac{28}{2} = 14 \, \text{cm}$

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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.