Answer:
Answer is D 312m^2
As D= 8m x 11m = A =88x 3 = 264+ 48 = 312
1/2 x 6 x 8 = 24
This makes triangle base of 6m
triangle side =8m
Rectangle side = 8m
and rectangle length = 11m
Explanation:
First finding
A= 6 x 11 = 66m^2 (rectangle area) or 10 x 9 = 90sq^2
A = 1/2 x 6 x 11 = 33 (1/2bh) triangle
33+ 33 + 66 +66 + 66 = 264 or 33+ 33+ 90+90+90 =336
As 336 was not in the answer we do not know what 10m/9m represents, we then see this triangle prism is not a normal shape and its length is same as its height
a) is not in usual proportions.
We try again reversing which makes triangle sides 10m+ base 9m
= 1/2 x 10 x 10 = 50m^2 = triangle face area
we cannot continue the reverse as the triangle sides do not match the rectangle height. We therefore have to use the first answer C 264m^2
As 10m, 9m <do not match >6m 11m 8m
However if the given sizes 10m, 9m = bases of two different rectangles we would calculate 2 faces and add them each to one unknown face being one of the other face sizes we found to make 3.
10 x 8 = 80
9 x 8 = 72
To make one of these SA totals for rectangles alone
=80+80+72=232 or 72+72+80 =224
Then add to the 33 m^2 triangles
= 232+ 33+ 33 =297m^2
= 224+33+33 =310m^2
We can now determine that these measurements represent irregular values and are not answers within multiple choice, however d) we can state the triangle is regular prism where triangle sides are regular too creating isosceles triangle 6,8,8,
8m x 11m = A =88x 3 = 264+ 48 = 312
1/2 x 6 x 8 = 24
As we have ruled out rectangle with side 8m x 11m + A (33m^2) of triangle would equal 310m^2 (88+88+88+33+33) =330m
And ruled out rectangle with side 8m x 6m= 48m^2 (48+48+48+33+33 =210sqm)
So therefore if triangles were to equal 1/2 x 6 x 8 = 24
24 x 3= 72sqm
add the rectangle amounts above
= 72 + 88+ 88+ 88 =336^2
try another way and we find D. here below.
answer D= 72+ 80+80+80 = 312m^2 this can makes a correct answer D.
As last rule out is;
72 + 72 +72 (+triangle of 72) =288^2 would be irregular as this is equal to (9 x 8) x 3 and then the 11m is not used. It is also not a listed answer. Therefore; D=312m^2 is correct.
A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.