If a right triangle has side lengths that measure 4 and 9, what is the length of the hypotenuse to the nearest hundredth (2 deci
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Answer:
Lateral Area = 624 square units
Surface area = 1,200 square units
Volume = 960 cubic units
Step-by-step Explanation:
==>Given:
Dimensions of the square pyramid as shown in the figure are:
length of 1 side of the square base (s) = 24
Slant height (l) = 13
Perpendicular height (h) = ?
==>Required:
a. Lateral area (L.A) = 4 × ½sl
b. Surface Area (S.A) = Base area (s²) × Lateral area (4 × ½sl)
c.Volume of the pyramid = ⅓ × Base area (s²) × perpendicular height (h)
==>SOLUTION:
a. Lateral area (L.A) = the area of the 4 lateral faces of the pyramid, which are triangular faces.
L.A = 4 × ½sl
From the figure given, s = 24; l = 13,
Therefore, L.A = 4 × ½ × 24 × 13
= 4 × 1 × 12 × 13
Lateral Area = 624 square units
b. Surface Area (S.A) = Base area (s²) × Lateral area (4 × ½sl)
Base area (s²) = 24² = 576 square units
Lateral area (4 × ½sl) = 624 square units
Therefore, total surface area = 576 + 624
= 1,200 square units
c. c.Volume of the pyramid using the formula ⅓ × Base area (s²) × perpendicular height (h)
Base area (s²) = 576 square units
Perpendicular height (h) is not given in the figure = h
Since already know the slant height (s), let's use Pythagorean theorem to find the perpendicular height (h) bearing in mind that a right triangle is formed in the middle of the pyramid as illustrated in the figure attached below.
The base of the right triangle = ½ of side length of the base (s) = ½ × 24 = 12
The hypotenuse (l) = 13
Therefore using the Pythagorean Theorem formula a² + b² = c², let's find the perpendicular height (h).
Where,
a² = h²
b² = (½s)² = 12²
c² = l² = 13²
Thus, h² + 12² = 13²
h² = 13² - 12²
h² = 169 - 144
h² = 25
h = √25
h = 5
==>Volume of pyramid (V) = ⅓ × Base area (s²) × perpendicular height (h)
V = ⅓ × 576 × 5
V = ⅓ × 2,880
V = 960 cubic units
