Let’s calculate each question step by step.
Question 1:
To find the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Given:
- Height = 8 inches
- Base = 32 inches
\[ \text{Area} = \frac{1}{2} \times 32 \times 8 = \frac{1}{2} \times 256 = 128 \text{ in}^2 \]
Answer: 128 in²
Question 2:
For the area of a right triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Given:
- Height = 6.25 yards (which is \( \frac{25}{4} \))
- Base = 22 yards
\[ \text{Area} = \frac{1}{2} \times 22 \times 6.25 = 11 \times 6.25 = 68.75 \text{ yds}^2 = 68 \frac{3}{4} \text{ yds}^2 \]
Answer: sixty eight and three fourths yds²
Question 3:
To find the total area of the deck after addition, add the area of the addition to the current area.
Area of the addition:
\[ \text{Area} = \text{length} \times \text{width} = 23.25 \times 14 = 325.5 \text{ ft}^2 \]
Total area:
\[ \text{Total Area} = 250 + 325.5 = 575.5 \text{ ft}^2 \]
Answer: 575.5 ft²
Question 4:
To find the area of the composite figure, one rectangle and one triangle are considered.
-
Rectangle Area:
\[ \text{Area}_{\text{rectangle}} = \text{base} \times \text{height} = 18 \times 8 = 144 \text{ m}^2 \]
-
Triangle Area (base = 6 m, height = 8 m):
\[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 8 = 24 \text{ m}^2 \]
-
Total area:
\[ \text{Total Area} = 144 + 24 = 168 \text{ m}^2 \quad (\text{Note: This does not match the options. Double-check inputs and methods used.}) \]
(In review, the problem appears to involve potentially more fundamental shapes or areas; I'll need further specifics for verification.)
Question 5:
To find the area of a four-sided shape with dimensions defined for height and widths measured, one can calculate the area of a trapezoid:
- Base1 = 15.4 yards
- Base2 = (4.6 + 10.8) = 15.4 yards
- Height = 9.3 yards
\[ \text{Area} = \frac{1}{2} \times (\text{Base1} + \text{Base2}) \times \text{Height} = \frac{1}{2} \times (15.4 + 15.4) \times 9.3 \]
\[ \text{Area} = 15.4 \times 9.3 = 143.22 \text{ yd}^2 \]
Answer: 143.22 yd²
Question 6:
Part A: Calculate the area of the brick paver border:
- Area of the outer rectangle:
\[ \text{Area}_{outer} = \text{length} \times \text{width} = 26 \times 14 = 364 \text{ ft}^2 \]
- Area of the inner rectangle (pool):
\[ \text{Area}_{inner} = 18 \times 6 = 108 \text{ ft}^2 \]
- Area of the border:
\[ \text{Area}{border} = \text{Area}{outer} - \text{Area}_{inner} = 364 - 108 = 256 \text{ ft}^2 \]
(Final calculations should note actual dimensions and overlaps of the shapes involved in this problem)
(Total area of border = 256 ft²)
Part B: To find the total cost of pavers needed:
\[ \text{Total Cost} = \text{Area}_{border} \times \text{Cost per ft}^2 \]
\[ = 256 \times 6 = 1536 \]
Total Cost = $1,536.00.