Question

Help me find the Lateral Area and the Surface Area

Answer 1

Good start.

Surface area:

Area of 2 trapezoids: 2 ((4+6)/2*4) = 40

Area of two side rectangles:
`2*9*√(17)=18√(17)` (I got root 17 from constructing a right triangle from the altitude just like last time and then finding the missing side using pythag)

Area of top rectangle: 4*9 = 36

Area of bottom rectangle: 6*9 = 54

Summing these up we get
`130+18√(17)`

Lateral area is the area excluding the bases (correct me if i'm wrong) so it will be
`130+18√(17)-40=90+18√(17)` (we need to subtract the areas of the trapezoids).

Answer 2

Explanation:

The lateral area consists of 2 trapezia and 2 rectangles.

= 2 * 1/2 * 4 *(4 + 6) + 2 * 9 * length of the sloping line

= 40 + 18 * length of the sloping line.

Find the length of the sloping lines:

Consider the right triangle whose height is 4 ft.

The trapezium is isosceles so the base of this triangle

= (6 - 4)/ 2 = 1 ft.

By Pythagoras:

Sloping line = √(1^2 + 4^2) = √17

So lateral area

= 40 + 18√17.

= 114.22 ft^2 to nearest hundredth

Total area =

40 + 18√17 + 4*9 + 6*9

= 130 + 18√17

= 204.22 ft^2 to nearest hundredth