solid figure

1.
first, heights of triangles with 2 different base are needed to figure out
consider triangle with base of 20cm,
height(h) can be found by Pythagoras' theorem
(h1)^2 + (20/2)^2 = 26^2 where h1 is height of triangle with base of 20cm
h1 = 24(cm)
similarly,
(h2)^2 + (16/2)^2 = 26^2 where h1 is height of triangle with base of 20cm
h2 = √612 = 6√17(cm)
total surface area
= 2*area of triangle with base of 20cm + 2*area of triangle with base of 16cm
+ area of base
=2(20*24/2) + 2(16*6*√17 / 2) + 20*16
=800+96√17 (cm^2)

2.
(a)
let P be the point on BC such that DP is perpendicular to BC
as ABCD is isosceles trapezium, BE = PC
=>2 * PC = BE + PC
=> PC = (BE + PC)/2
=> PC = (BC - EP)/2
EC
= EP + PC
= EP + (BC - EP)/2
= (BC+EP)/2
= (BC+AD)/2 (EP and AD are opposite sides of rectangle so EP = AD)
= (20+8)/2
= 14 (cm)
as AEC is isosceles triangle, AE = EC = 14(cm)
(b)
volume of the prism
= [(8+20)(14)/2](25)
= 4900 (cm^2)

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