Question

I dont understand TwT pls help me it makes me understand better and learn from it. it truly helps me

Answer 1

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