Step-by-step explanation:
oh, come on this is really simple.
let's start with the volumes.
the volume is any fully symmetrical 3D object is
base area × height
yes, that applies to both, as the triangular prism of 2. is just on its side. image it stands on one of the triangle sides, and it is all the same again.
the base area of 1. is a 3×4 rectangle (we can use the prism as it stands), and its volume is
3×4×5 = 60 ft³
you remember that the area of a rectangle is
length × width ?
the base area of 2. is as mentioned one of the right-angled triangles.
the area of a triangle is
baseline × height / 2
and for a right-angled triangle we can use its legs for baseline and height.
so, we get for the volume
4×3/2 × 7 = 2×3×7 = 6×7 = 42 cm³
now for the surface areas :
they are the sum of the areas of all sides.
1. has 6 sides in 3 pairs of equal sides :
top and bottom = 2 × 3×4 = 24 ft²
left and right = 2 × 4×5 = 40 ft²
front and back = 2 × 3×5 = 30 ft²
in total, the surface area is
24+40+30 = 94 ft²
2. has only 5 sides
top and bottom triangles = 2 × 4×3/2 = 12 cm²
a left side = 4×7 = 28 cm²
a right side = 5×7 = 35 cm²
a back side = 3×7 = 21 cm² (which it stands on in the graphic)
in total the surface area is
12+28+35+21 = 96 cm²
