A cuboid has total surface area of 40 meter squar and its lateral surface area is 26 meter squar .Find the area of its surface
Total surface area-lateral surface area
= 2*(surface of top + surface of bottom)
40-26
2*(surface of top + surface of bottom)=14
surface of top (or bottom) = 14/2=7
Surface area =2(L+b)×h
T.S.A=2(lb+bh+lh)
lb+bh+lh= 40/2 [eq 1]
L.S.A= 2h(l+b)
26/2=lh+bh [eq 2]
from eq 1&2 we get,
lb+13=20
lb=7cm
To find the surface area of a cuboid, we need to consider the total surface area and the lateral surface area.
The total surface area of a cuboid is the sum of the areas of all its faces. It can be calculated using the formula:
Total Surface Area = 2 * (Length * Width + Width * Height + Height * Length)
In this case, we are given that the total surface area of the cuboid is 40 square meters:
40 = 2 * (Length * Width + Width * Height + Height * Length)
We are also given that the lateral surface area of the cuboid is 26 square meters:
26 = 2 * (Width * Height)
Let's solve these equations to find the values of Length, Width, and Height:
Step 1: Dividing the equation for lateral surface area by 2, we get:
13 = Width * Height
Step 2: Substitute this value into the equation for total surface area:
40 = 2 * (Length * Width + Width * Height + Height * Length)
40 = 2 * (Length * Width + 13 + Length * Height)
Step 3: Simplify the equation:
20 = Length * Width + 13 + Length * Height
20 - 13 = Length * Width + Length * Height
7 = Length * Width + Length * Height
Step 4: Factor out the common term, Length:
7 = Length * (Width + Height)
Step 5: We can now solve for Length by dividing both sides of the equation by (Width + Height):
Length = 7 / (Width + Height)
Step 6: Substitute this value of Length back into the lateral surface area equation:
13 = Width * Height
Step 7: We can solve for Width or Height, since we now know the relationship between them. Let's solve for Width:
Width = 13 / Height
Step 8: Substitute these values of Length and Width back into the total surface area equation:
40 = 2 * (Length * Width + Width * Height + Height * Length)
40 = 2 * ((7 / (Width + Height)) * (13 / Height) + (13 / Height) * Height + 7)
40 = 2 * (91 / (Height * (Width + Height)) + 13 + 7)
40 = 2 * (91 / (13 + Height) + 13 + 7)
Step 9: Simplify the equation to find the value of Height:
40 = 2 * (91 / (13 + Height) + 20)
40 = 2 * (91 + 20 * (13 + Height)) / (13 + Height)
40 * (13 + Height) = 2 * (91 + 20 * (13 + Height))
40 * (13 + Height) = 2 * (91 + 260 + 20 * Height)
40 * (13 + Height) = 2 * (351 + 20 * Height)
40 * (13 + Height) = 2 * 351 + 2 * 20 * Height
40 * (13 + Height) = 702 + 40 * Height
40 * 13 + 40 * Height = 702 + 40 * Height
520 = 702
So, the surface area cannot be determined with these given measurements. There seems to be an error in the given information or calculations. Please recheck the values or provide additional information to correctly calculate the surface area.