Answer:
d = 16
Step-by-step explanation:
15 = d-1
Add 1 to each side
15 +1 =d-1+1
16 =d
It's just asking for the gradient basically
150/3 = 50
Or technically -50 because it's decreasing
Answer:
<h3>Figure 1</h3>
- Perimeter of base = 5 + 5 + 8 = 18 ft
- Base area = 1/2(8)(3) = 12 ft²
<u>Surface area:</u>
- S = 18*7 + 2*12 = 150 ft²
<h3>Figure 2</h3>
<u>Surface area of cube:</u>
- S = 6a² = 6(2.5)² = 37.5 m²
<u>Surface area of prism:</u>
- S = 2(11 + 9)(7) = 280 m²
<u>Overlapping area:</u>
<u>Surface area of composite figure:</u>
- S = 280 + 37.5 - 2(6.25) = 305 m²
Answer:
24.5 unit²
Step-by-step explanation:
Area of ∆
= ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |
= ½ | (-1)(3 -(-4)) + 6(-4 -3) + (-1)(3 - 3) |
= ½ | -7 - 42 |
= ½ | - 49 |
= ½ (49)
= 24.5 unit²
<u>Method 2:</u>
Let the vertices are A, B and C. Using distance formula:
AB = √(-1-6)² + (3-3)² = 7
BC = √(-6-1)² + (-4-3)² = 7√2
AC = √(-1-(-1))² + (4-(-3))² = 7
Semi-perimeter = (7+7+7√2)/2
= (14+7√2)/2
Using herons formula:
Area = √s(s - a)(s - b)(s - c)
here,
s = semi-perimeter = (14 + 7√2)/2
s - a = S - AB = (14+7√2)/2 - 7 = (7 + √2)/2
s - b = (14+7√2)/2 - 7√2 = (14 - 7√2)/2
s - c = (14+7√2)/2 - 7 = (7 + √2)/2
Hence, on solving for area using herons formula, area = 49/2 = 24.5 unit²
