Question

In a right rectangular pyramid with base edges a=18 cm and b=10 cm the slant height towards a is k=13 cm while the slant height towards b is l=15 cm. Find the surface area of a prism

Answer 1

Surface Area of pyramid=(sum of four isosceles triangle)+ rectangular base
                     =(a*k+b*I) + a*b
                     =(18*13+10*15)+ 18*10
                     =564 cm²

Answer 2

Answer:

The surface area of a pyramid is 564 cm².

Step-by-step explanation:

It is given that the rectangular base of the pyramid has dimensions 18 cm and 10 cm. The slant height towards a is k=13 cm while the slant height towards b is l=15 cm.

Area of a rectangle is

$A=length\times width$

The area of base is

$A_1=18\times 10=180$

The area of a triangle is

$A=\frac{1}{2}\times base \times height$

Area of a triangle with base 18 and height 13 is

$A_2=\frac{1}{2}\times 18 \times 13=117$

Area of a triangle with base 10 and height 15 is

$A_3=\frac{1}{2}\times 10 \times 15=75$

Total surface area of a pyramid is

$A_1+2(A_2)+2(A_3)=180+2(117)+2(75)=564$

Therefore the surface area of a pyramid is 564 cm².