Question

can someone can help me

Answer 1

Answers:

1) $40 units^{2}$

2) $37.5 units^{2}$

Step-by-step explanation:

1)The surface are of this square pyramid is the area of the triangle multiplied by 4 (since there are 4 triangles) plus the area of the square:

$A_{pyramid}=4(A_{triangle})+A_{square}$ (1)

Now, the area of a triangle is given by:

$A_{triangle}=\frac{(b)(h)}{2}$ (2)

Where:

$b=4 units$ is the base

$b=3 units$ is the height

$A_{triangle}=\frac{(4 units)(3 units)}{2}=6 units^{2}$ (3)

The area of a square is:

$A_{square}=L^{2}$ (4)

Where $L=4$ is the length of each side of the square

$A_{square}=(4 units)^{2}=16 units^{2}$ (5)

Then, substituting (3) and (5) in (1):

$A_{pyramid}=4(6 units^{2})+16 units^{2}$ (6)

$A_{pyramid}=40 units^{2}$ (7)

2) The surface area of a cube is:

$A_{cube}=6(l^{2})$ (8)

Where $l=2.5 units$ is the length of each edge

Then:

$A_{cube}=6((2.5 units)^{2})$ (9)

$A_{cube}=37.5 units^{2}$ (10)