Question 1078574
The lateral area and total area would require knowing the size of that square base.
The problem does not provide that information directly,
but the length, {{{s}}} , of the base sides
can be calculated from the information given.
A top view, and a cross section of the pyramid
(cutting across the middle of opposite lateral faces)
would look like square and the isosceles triangle below
{{{drawing(400,350,-16.5,15.5,-2,26,
green(triangle(-8,7,-15,7,-15,0)),
triangle(-1,0,-15,14,-15,0),
triangle(-1,14,-15,14,-15,0),
rectangle(-1,0,-15,14),
green(triangle(8,24,8,0,1,0)),
green(rectangle(7.5,0.5,8,0)),
triangle(8,24,15,0,1,0),
locate(8.2,11,green(24)),
locate(-16,8,A),locate(-8.3,6.5,B),
locate(-8.3,8.5,C),locate(0.5,0,A),
locate(7.7,0,B),locate(7.7,25,C),
locate(4.5,12,25),
locate(-13,7,green("s / 2")),
locate(4,1.3,green("s / 2"))
)}}} Applying the Pythagorean theorem to right triangle ABC,
{{{(s/2)^2+24^2=25^2}}} --> {{{(s/2)^2+576=625}}} --> {{{(s/2)^2=625-576}}} --> {{{(s/2)^2=49}}} --> {{{s/2=7}}}  --> {{{s=14}}} .
The {{{4}}} lateral faces are triangles with base {{{s=14}}} and height {{{25}}} ,
so the lateral area is
{{{4*(14*25/2)=highlight(700)}}} square units
(of whatever units was used to measure pyramid height and slant height).
The area of the square base is {{{14^2=196}}} square units,
so the total area (in square units) is
{{{700+196=highlight(896)}}} square units.