Exercise 17 Page 620

a To find the area of the paved surface, we will add the areas of the driving region and the four parking spaces.

We see that the driving region is a rectangle with a base of $50 feet$ and a height $15 feet,$ and that each of the parking spaces is a parallelogram with a base of $10 feet$ and height $16 feet .$ Let's use the area formula, $A = b h,$ to find the areas of each of these sections.

Area, $A$	$b h$	$A = b h$
Driving region, $A_{d}$	$50 \cdot 15$	$A_{d} = 750$
Parking space, $A_{p}$	$10 \cdot 16$	$A_{p} = 160$

Now, we can find the total area of the paved surface,

A .

Remember that there are four parking spaces.

A = A_{d} + 4 \cdot A_{p} ⇓ A = 750 + 4 \cdot 160 = 1390

The paved surface has an area of

1390 ft^{2} .

b To find the area

A

of the paved surface, we can first find the area

A_{E}

of the entire parking lot, which is a

31

feet by

50

feet rectangle. Then, we can subtract the area

A_{t}

of the two flower spaces from the entire area.

A = A_{E} - 2 \cdot A_{t}

c Let's first find the total area

A_{E}

of the entire parking lot. It is a rectangle with the dimensions

50 feet

31 feet,

so its total area is

1550 ft^{2} .

A_{E} = b h ⇓ A_{E} = 50 \cdot 31 = 1550

Now, we need to find the areas of the two triangular flower spaces. Let's focus on the left triangle first. Since the parking spaces are congruent, the total base length of the four parallelograms is

40 feet .

This means that the base of the triangle is

10 feet .

Therefore, the area

A_{t}

of the left triangle is

80 ft^{2} .

A_{t} = \frac{1}{2} b h ⇓ A_{t} = \frac{1}{2} 10 \cdot 16 = 80

Given that the triangles are congruent, the total area for the flower spaces,

2 A_{t},

160 ft^{2} .

By subtracting this area from the entire area

A_{E},

we can find the area

A

of just the paved surface.

A = A_{E} - 2 \cdot A_{t} ⇓ A = 1550 - 160 = 1390

The paved surface has an area of

1390 ft^{2} .

We ended with the same result as in Part A, so our method is correct.

Subchapter links

Lesson Check p.619

Practice and Problem-Solving Exercises p.619-621

Standardized Test Prep p.622

Mixed Review p.622