Question

Hey plz help and show work

Answer 1

The dog house consists of two geometric objects, triangular prism and rectangular prism.

First, find the surface area of triangular prism
The triangular prism consists of
base of triangle (b) = 3 ft
height of triangle (h) = 2.5 ft
height of prism or length of rectangle (l) = 4 ft
side of triangle or width of rectangle (w) = 2.5 ft

Now, calculate the area
area of tp = area of two triangle + area of 2 rectangle
area of tp = (2 × 1/2 × b × h) + (2 × l × w)
area of tp = (2 × 1/2 × 3 × 2) + (2 × 4 × 2.5)
area of tp = 6 + 20
area of tp = 26 ft²

Second, find the surface area of rectangular prism
The rectangular prisms consists of
length (l) = 3 ft
width (w) = 4 ft
height (h) = 2 ft

Now, calculate the area
area of rp = area of back and front rectangle + area of left and right rectangle
area of rp = (2 × l × h) + (2 × w × h)
area of rp = (2 × 3 × 2) + (2 × 4 × 2)
area of rp = 12 + 16
area of rp = 28 ft²

Third, add both of the area
area = area of tp + area of rp
area = 26 + 28
area = 54 ft²

The area of the dog house is 54 ft²