Question

A cuboid is there with dimensions 8 cm*6cm*2cm if the cuboid is cut vertically along the diagonal of the upper face into two equal parts then what is the total surface area of any one of the two parts​

Answer 1

Answer:

Step-by-step explanation:

When the cube shown above , is cut along diagonal FC , it will be divided into 2 right isosceles triangular prisms.

And when cut along diagonal DE, each piece will further be divided into 2 more isosceles right triangular prisms.

TO FIND: Total Surface area of Prism APBQDC

Top surface DCEF ia a square surface with each side 8 cm . <FDC = 90°

So, diagonal FC = √(8² + 8² ) = √128 = 8√2 cm

=> DQ = QC = 4√2 ( as diagonals of a square are equal & bisect each other at 90° angle.

Now, our required prism is APBDQC , which has following faces.

(1) Square ABCD , area = 8 * 8 = 64 cm²

(2) Rectangle APQD, area = 8 * 4√2 = 32√2 cm²

(3) Rectangle PBCQ, area = 8 * 4√2 = 32√2 cm²

(4) Isosceles Right triangle DQC, right angled at Q & DQ = CQ , area = 1/2* 4√2 * 4√2 = 16 cm²

(5) Similarly area ( triangle APB) = 16 cm²

So, total surface area = 64+32√2 +32√2+16+16

= 96 + 64√2

= 96 + 64* 1.41 = 96 + 90.24

= 186. 24 cm² ( approx)