Respuesta :

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[tex]A_1=4cm\cdot4cm=16cm^2\\\\A_2=\dfrac{4cm\cdot6cm}{2}=\dfrac{24cm^2}{2}=12cm^2\\\\The\ surface\ area\ of\ pyramid:\\\\A_S=A_1+4A_2\\\\A_S=16cm^2+4\cdot12cm^2=16cm^2+48cm^2=64cm^2[/tex]

Answer:

64 cm²

Step-by-step explanation:

To find the area of the square pyramid:

We use the formula;

Area of the square pyramid =   B + [tex]\frac{1}{2}[/tex]  p . l

Where b = area of the base

p = perimeter

l = slant height

Area of base =  length × breadth

                        =  4 cm  ×   4 cm  

                        =  16 cm²

slant height is given as 6 cm

Perimeter =  4 cm + 4 cm + 4 cm + 4 cm = 16 cm

Now we can plug all our variable into the formula;

Area of the square pyramid =   B + [tex]\frac{1}{2}[/tex]  p . l

                                               

                                               =16 cm² + [tex]\frac{1}{2}[/tex]  ×  16 cm  × 6 cm

                                                = 16 cm²  +  48 cm²

                                                  =  64 cm²

(   Note; the value of [tex]\frac{1}{2}[/tex]  ×  16 cm  × 6 cm = 48 cm²)

Therefore the surface area of the pyramid is 64 cm²

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