Fine the lateral area of the hexagonal pyramid
1 answer:
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Answer:
A. The length of the second leg is 8.5 inches
B. The length of the three-dimensional diagonal is 9.9 inches
Step-by-step explanation:
Let us revise the relation between the hypotenuse and the two legs of a right triangle
(hypotenuse)² = (vertical leg)² + (horizontal leg)²
∵ The length of the rectangular box = 8 inches
∵ The width of the rectangular box = 3 inches
∵ The height of the rectangular box = 5 inches
∵ Length and width are perpendicular to each other
∴ The Δ whose legs are 3 and 8 is a right triangle
In the right Δ whose legs are 3 and 8
∵ (hypotenuse)² = (3)² + (8)²
∴ (hypotenuse)² = 9 + 64
∴ (hypotenuse)² = 73
- Take √ for both sides
∴ hypotenuse = = 8.544003745
- Round it to the nearest tenth of one inch
∴ hypotenuse = 8.5 inches
A.
The 3-dimensional diagonal is the hypotenuse of a right triangle whose legs are the vertical edge and the hypotenuse of the right triangle whose legs are 3 and 8
∵ The hypotenuse of the right triangle whose legs are 3 and
8 is 8.5 inches
∴ The length of the second leg is 8.5 inches
B.
In the right triangle whose hypotenuse is the 3-dimensional diagonal and legs are the vertical edge , the hypotenuse of the right triangle whose legs are 3 and 8
∵ (3-dimensional diagonal)² = (5)² + (73)²
∴ (3-dimensional diagonal)² = 25 + 73
∴ (3-dimensional diagonal)² = 98
- Take √ for both sides
∴ 3-dimensional diagonal = = 9.899494937
- Round it to the nearest tenth of an inch
∴ 3-dimensional diagonal = 9.9 inches
∴ The length of the three-dimensional diagonal is 9.9 inches
<em>V.I.N: you can find the length of the three-dimensional diagonal by using this rule → </em><em> </em>
Answer:
1240.4 mm²
Step-by-step explanation:
The surface area of a pyramid = Area of the all sides + Area of base
Each side is a triangle.
With a regular pentagonal pyramid, the area of each triangle is
For the 5 triangles,
Substituting given values,
Area of base = 440.4 mm²
Surface area of a pyramid = 800 + 440.4 mm² = 1240.4 mm²