Question

1. Find the area of the trapezium whose parallel sides are 22 cm and 31 cm respectively, and the distance between them is 12 cm.

2. The area of a trapezium is 320 sq.cm and distance between the parallel sides is 20 cm.if one of the parallel sides is 16 cm,find the length of another parallel side.

3. Find the area of a rhombus if:

a) Each side is 16 m and height is 9 m
b) Each diagonals are 20 cm and 18 cm.

4. The area of a rhombus is 256 sq.cm and one of the diagonals is 32 cm.find the length of other diagonal.

5. The area of a triangle with a base of 8 cm is 24 sq.cm.find its altitude from this base.

6. Find the lateral surface area,total surface area and volume of a cube of:

a) Side=70cm

b)side=25cm​

Answer 1

1.

Given:

parallel sides are 22 cm and 31 cm respectively, and the distance between them is 12 cm.

To find:

Area of trapezium ?

Solution:

Formula for area of trapezium

$A =\dfrac{1}{2}\times \text{Sum of parallel sides}\times \text{Distance between parallel sides}$

$\Rightarrow A = \dfrac{1}{2}\times (22+31)\times 12 = 318\ sq\ cm$

2.

Given:

The area of a trapezium is 320 sq.cm and distance between the parallel sides is 20 cm.one of the parallel sides is 16 cm

To find:

length of another parallel side?

Solution:

Let the other parallel side = x cm

Formula for area of trapezium

$A =\dfrac{1}{2}\times \text{Sum of parallel sides}\times \text{Distance between parallel sides}$

$320=\dfrac{1}{2}\times (16+x)\times 20\\\Rightarrow x = 16\ cm$

3. a)

Given:

Rhombus with Each side is 16 m and height is 9 m

To find:

Area of rhombus ?

Solution:

Formula for area of rhombus:

$A = Base \times Height$

$\Rightarrow A =16\times 9 =144\ sq\ m$

b)

Given:

Rhombus with Each diagonals are 20 cm and 18 cm.

To find:

Area of rhombus ?

Solution:

Formula for area of rhombus:

$A = \dfrac{1}{2}\times d_1\times d_2\\\Rightarrow A = \dfrac{1}{2}\times 20 \times 18 = 180\ sq\ cm$

4.

Given:

Area of rhombus = 256 sq cm

One diagonal 32 cm

To find:

Length of other diagonal ?

Solution:

Formula for area of rhombus:

$A = \dfrac{1}{2}\times d_1\times d_2\\\Rightarrow 256 = \dfrac{1}{2}\times 32 \times d_2\\\Rightarrow d_2 = 16\ cm$

5.

Given:

The area of a triangle with a base of 8 cm is 24 sq.cm.

To find:

Altitude of triangle ?

Solution:

Formula for area of triangle:

$A = \dfrac{1}{2}\times Base\times Altitude\\\Rightarrow 24 = \dfrac{1}{2}\times 8\times Altitude\\\Rightarrow Altitude = 6\ cm$

6.

a)

Given:

Side of cube = 70 cm

To find:

Volume, lateral surface area, total surface area of cube?

Solution:

Volume = $Side^3$ = $70^3 = 343000\ cm^3$

Lateral surface area = $4\times side^2 = 4\times 70^2 = 19600\ cm^2$

Total surface area = $6\times side^2 = 6\times 70^2 = 29400\ cm^2$

b)

Given:

Side of cube = 25 cm

To find:

Volume, lateral surface area, total surface area of cube?

Solution:

Volume = $Side^3$ = $25^3 = 15625\ cm^3$

Lateral surface area = $4\times side^2 = 4\times 25^2 = 2500\ cm^2$

Total surface area = $6\times side^2 = 6\times 25^2 = 3750\ cm^2$

Answer 2

Answer:

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