Test: Mensuration- 1 - Class 8 MCQ

Base and height of ΔABF and ΔCED are same. Thus their respective areas will be same.

Total area = (Area of △ABF)×2+Area of rectangle BCEF

Total area = (1/2×10×6)×2+(10×20) = 60+200

Total area = 260cm²

Area of Trapezium Derivation Using a Parallelogram: 
To derive the formula for the area of a trapezium using parallelogram, we will consider two identical trapeziums, each with bases a and b and height h. Let A be the area of each trapezium. Assume that the second trapezium is turned upside down as shown in the figure below.

We can see that the new figure obtained by joining the two trapeziums is a parallelogram whose base is a + b and whose height is h. We know that

• the area of a parallelogram is base × height = (a + b) h.
• the area of the above parallelogram in terms of 'A' is, A + A = 2A.

Thus, 2A = (a + b) h

⇒ A = (a+b)h/2

Thus, the formula for the area of a trapezium is derived. where a and b are parallel sides and h is height.

Area of Rectangle = Length * Breadth.
Area of Rhombus Using DiagonalsA = ½ × d₁ × d₂
Area of quadrilateral willl be calculated based on which type of quadriateral it is-
Area of trapezium willl be 1/2 (sum of Parallel sides )*height.

Given that, the length of one side of the trapezium b1 = 6cm and another is b2 =14cm.
The height of the trapezium h = 5cm.
Drawing the figure from the given data.

Area of Trapezium  = 1/2 (sum of Parallel sides ) * height
let a and b are the parallel sides:
a= 4cm
b= 6 cm
h= 3cm
according to formula -> 1/2(4+6)*(3)
=>1/2(10)(3)
=>30/2
=>15 cm²

Total surface area = 2 (20 x 15 + 20 x 10 + 10 x 15)

TSA = 2(300 + 200 + 150) = 1300 cm²

Volume of a cuboid = Base area × Height
Height = Volume / Base area
H = 275/25 = 11 cm

Total surface area = 2πr (h + r)
968 = 2 x 22/7 x 7 (7+h)
h = 15 cm

Total surface area = 2πr (h + r)
= 2π 5 (10 + 5) = 150π cm².

Lets break the figure -
It has 6 surfaces.
Area of bottom surface = L * B
Area of Top Surface = L * B
Area of Right side surface = B * H
Area of Left Side surface  = B * H
Area of front Surface = H * L
Area of Back surface = H * L 
Total surface area of Cuboid = sum of all the surfaces.
=> (Bottom surface area + Top surface area + Right side surface area + Left side surface area + front side surface area
back side surface area)
=> (LB + LB + BH + BH + HL + HL)
=> (2LB + 2BH + 2HL)
=> 2(LB + BH + HL)
hence option B is correct.

Lateral surface area -> Total Surface area of cuboid - surface area of Top and Bottom Surfaces.
=> 2LB + 2BH + 2HL - LB - LB
=> 2BH + 2HL
=> 2H(L + B)
hence option A is correct 

Since all side is cube is same 
so the volume of cube is = side of cube * side of Cube * side of cube
lets take side of cube = l 
=> l*l*l
=> l³ 
Hence the correct option is A

Base area = length * breadth = 20 sq.cm
Now,
Volume of cuboid = length * breadth * height
Volume = 20 * height
200 = 20 * height
Height = 200 / 20 = 10 cm.

Lets  take the original side of cube be S, and final side be 2S.
Orginal surface area will be => 6 * S * S
Final surface area will be => 6 * 2S * 2S
=> 4 * (6 * S * S)
=> 4 times orginal surface area.
Hence the option C is correct.

Total surface area of a cylinder = πr²+2πrh+πr²=2πr(r+h)

Area of rhombus is ½* d1*d2 =6*8/2=24cm².

Base =  7 cm and Height  = 4 cm
Area of  Rhombus = Base×Height
= 7 * 4
= 28 cm²

Volume of the cuboid = L * B * H 
V = 4cm * 2cm * 3cm
V = 24 cm³ 
Hence the option A is correct.