Question

4. Find the lateral area and surface area of the given prism.

11.Find the volume of the square pyramid.

Answer 1

Q4. S.A. = 752.28 m²

Q11. V = 384 ft³

Explanation:

`\bold{Q4}\\\text{We have}\\\text{two right triangles with legs a = 4m and b = 7m}\\\text{three rectangles}\ 7m\ * 38m,\ 8.06m\ *\ 38m\ \text{and}\ 4m\ *\ 38m\\\\\text{The formula of an area of a right triangle:}\\\\A=(ab)/(2)\\\\\text{substitute:}\\\\A_1=((4)(7))/(2)=(28)/(2)=14\ m^2\\\\\text{The formula of an area of a rectangle}\ l\ * w:\\\\A=lw\\\\\text{substitute:}\\\\A_2=(7)(38)=266\ m^2\\A_3=(8.06)(38)=306.28\ m^2\\A_4=(4)(38)=152\ m^2\\\\\text{The Surface Area:}`

`S.A.=2A_1+A_2+A_3+A_4\\\\S.A.=2(14)+266+306.28+152=752.28\ m^2`

`\bold{Q11}\\(look\ at\ the\ picture)\\\\\text{The formula of a volume of a pyramid:}\\\\V=(1)/(3)BH\\\\B-\text{area of a base}\\H-\text{height}\\\\\text{In the base we have the square. The formula of an area of a square with side a:}\\\\A=a^2\\\\\text{We have}\ a=12ft.\ \text{Substitute:}\\\\B=12^2=144\ ft^2\\\\\text{For}\ H\ \text{we need use the Pythagorean theorem:}\\\\H^2+6^2=10^2\\\\H^2+36=100\qquad\text{subtract 36 from both sides}\\\\H^2=64\to H=√(64)\\\\H=8\ m`

`\text{Substitute:}\\\\V=(1)/(3)(144)(8)=(48)(8)=384\ ft^3`