Question

In the given figure, if ZDBC = 80º and ZBAC = 40°, then find ZBCD. Further, if AB = BC, then find ZECD
[31
80%
B
10H
The lonnth hreadth and height of a cuboid are 8 m, 6 m and 4 m respectively. Find its total surface area.​

Answer 1

||✪✪ QUESTION ⓵ ✪✪||

Given :-

• Angle DBC = 80°.
• Angle BAC = 40°
• AB = BC
• Angle ECD ?

|| ✰✰ ANSWER ✰✰ ||

Since, we have AB = BC ,

So, in isosceles ∆ABC,

→ Angle BAC = Angle ACB = 40° ( Angle Opposite to Equal sides are Equal ). -------------- Equation (1)

Now,

→ Angle BAC = Angle BDC = 40° . ( The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.) ---- Equation (2)

_________

Now, in ∆BDC, we have ,

→ Angle CBD = 80° (Given).

→ Angle BCA = 40° ( From Equation (1) )

→ Angle BDC = 40° (From Equation (2))

Now, we know that, sum of all interior angles of a ∆ is 180° .

So, in ∆BDC,

→ Angle CBD + Angle BCA + Angle BDC + Angle ECD = 180°

→ 80° + 40° + 40° + Angle ECD = 180°

→ Angle ECD = 180° - 160°

→ Angle ECD = 20° (Ans).

Hence, Angle ECD is Equal to 20°.

______________________________

||✪✪ QUESTION ❷ ✪✪||

The length breadth and height of a cuboid are 8 m, 6 m and 4 m respectively. Find its total surface area. ?

|| ✰✰ ANSWER ✰✰ ||

we know that Total surface Area of cuboid is given by :-

☛ 2[ Length * Breadth + Breadth *Height + Height * Length]

Putting values we get,

☞ TSA = 2[ 8*6 + 6*4 + 4*8 ]

☞ TSA = 2[ 48 + 24 + 32 ]

☞ TSA = 2 * 104

☞ TSA = 208m²

Hence, TSA of Cuboid is 208m².

Answer 2

ANSWER (1) :-

Given that AB = BC ,

So, in isosceles ∆ABC,

=> Angle BAC = Angle ACB = 40° ( Angle Opposite to Equal sides are Equal ).

Also

=> Angle BAC = Angle BDC = 40° . ( The angles at the circumference subtended by the same arc are equal.)

in ∆BDC now, we have ,

→ Angle CBD = 80° (Given).

→ Angle BCA = 40°

→ Angle BDC = 40°

we know that sum of all interior angles of a ∆ is 180° .

So, in ∆BDC,

=> Angle CBD + Angle BCA + Angle BDC + Angle ECD = 180°

=> 80° + 40° + 40° + Angle ECD = 180°

=> Angle ECD = 180° - 160°

=> Angle ECD = 20°

So, Angle ECD is Equal to 20°.

______________________________

QUESTION 2 :-

The length breadth and height of a cuboid are 8 m, 6 m and 4 m respectively. Find its total surface area. ?

ANSWER :-

Formula used = 2[ Length * Breadth + Breadth *Height + Height * Length]

Putting values ,

=> TSA = 2[ 8*6 + 6*4 + 4*8 ]

=> TSA = 2[ 48 + 24 + 32 ]

=> TSA = 2 * 104

=> TSA = 208m²