Question 857827
{{{h}}}= height of the cuboid, in cm.
{{{drawing(300,300,-3.5,4.5,-1,7,
line(0,0,0,3),line(0,0,-2,1),line(0,0,3,2),
line(-2,1,-2,4),line(3,2,3,5),line(3,5,1,6),
line(-2,4,1,6),line(-2,4,0,3),line(0,3,3,5),
locate(-1.5,0.5,5cm),locate(1.3,1,10cm),locate(0.1,1.7,h)
)}}} The area of the base and the area of the top are each
{{{(5cm)(10cm)=50}}}{{{cm^2}}}
The perimeter of the base is
{{{5cm+10cm+5cm+10cm=30cm}}}
and that times the height {{{h}}} would be the lateral area
(the area of the 4 vertical faces), which (in square centimeters) would be
{{{30h}}}
The total surface area of the cuboid (in square centimeters) is
{{{50+50+30h=280}}}
{{{100+30h=280}}}
{{{30h=280-100}}}
{{{30h=180}}}
{{{h=180/30}}}
{{{highlight(h=6)}}}
The height of the cuboid is {{{highlight(6cm)}}} .