Question

What is the total surface area of the rectangular pyramid below

Answer 1

Answer:

Total surface area of the pyramid = 225 ft²

Step-by-step explanation:

Total surface area of the given pyramid is defined by  

(Area of rectangular base) + 2(area of two triangular sides with height 8 ft and base 12 ft) + 2(area of two triangles with height 9.5 ft and base 6 ft)

Total surface area = (12×6) + 2[$\frac{1}{2}\times(h)(b)$]+2[$\frac{1}{2}\times(h')(b')$]

= 72 + 2[$\frac{1}{2}\times(8)(12)$]+2[$\frac{1}{2}\times(9.5)(6)$]

= 72 + 96 + 57

= 225 ft²

Therefore, total surface area of the pyramid is 225 ft²

Answer 2

Answer:

S.A. = 225 ft²

Step-by-step explanation:

We have

the rectangle 12ft × 6ft

two triangles with the base b = 12ft and the height h = 8ft

two triangles with the base b = 6ft and the height h = 9.5ft.

The formula of an area of a rectangle l × w:

$A=lw$

Substitute:

$A_1=(12)(6)=72\ dt^2$

The formula of an area of a triangle:

$A=\dfrac{bh}{2}$

Substitute:

$A_2=\dfrac{(12)(8)}{2}=48\ ft^2$

$A_3=\dfrac{(6)(9.5)}{2}=28.5\ ft^2$

The Surface Area:

$S.A.=A_1+2A_2+2A_3$

Substitute:

$S.A.=72+2(48)+2(28.5)=225\ ft^2$