Question

the figure shows the cross section of the middle part of a thermos flask the top part is a trapezium the middlepart rectangle and the bottom is a semicircle if CE=20 CM ,BC equals to 25 CM AB is equals to GF equals to 13 cm AG=10CM and an=12CM find the perimeter the area of the cross section

Answer 1

Answer:

Perimeter of the cross section = 120.4 cm

Area of the cross section = 837 cm²  

Solution:

Given CE = 20 cm, BC = 25 cm,

AB = GF = 13 cm

AG = 10 cm, AN = 12 cm

Radius of the semi-circle = 20 ÷ 2 = 10 cm

Perimeter of CE = πr

                          = 3.14 × 10

                          = 31.4 cm

Perimeter of the cross section = AB + BC + CE + EF + FG + GA

                                                  = 13 cm + 25 cm + 31.4 + 25 + 13 + 13

                                                  = 120.4 cm

Perimeter of the cross section = 120.4 cm

Formulas:

Area of the trapezium =      

$\frac{1}{2} \ \times sum \: of \: the \: parallel \: side \: \times height$

                       

Area of the rectangle = length × width

Area of the semi-circle =

$\frac{1}{2} \times\pi \:r {}^{2}$

Area of the cross section = Area of the trapezium + Area of the rectangle

                                             + Area of the semi-circle

                           

$= \frac{1}{2} \times (10 + 20)12 + (25 \times20) + ( \frac{1}{2} \times 3.14 \times 10)$

                                         = 180 cm² + 500 cm² + 157 cm²

                                         = 837 cm²

Area of the cross section = 837 cm²  

Answer 2

Correct Question :

The figure; shows the cross section of the middle part of a thermos flask the top part is a trapezium the middlepart rectangle and the bottom is a semicircle. If CE=20 cm, BC = 25 cm AB is equals to GF equals to 13 cm AG =b10 cm and AN=12 cm. Then, find the perimeter and the area of the cross section.

Answer :

Perimeter = 120.4 cm

Area of cross-section = 837 cm²

$\rule{200}2$

Explanation :

i) CED is a semi-circle having diameter 20 cm.

So, radius = diameter/2 = 20/2 = 10 cm

Now,

The perimeter of CE = πr

→ 22/7 × 10

→ 31.4 cm

Now, Perimeter of AGEC = AB + BC + CE + EF + FG + GA

Substitute the known values

→ 13 + 25 + 31.4 + 25 + 13 + 10

→ 120.4 cm

ii) Area of cross-section = Area of trapezium + Area of rectangle + Area of semi-circle

Area of trapezium = 1/2 (sum of parallel sides) × height

→ 1/2 × (10 + 20) × 12

→ 6(30)

→ 180 cm²

Area of rectangle = length × breadth

→ 25 × 20

→ 500 cm²

Area of semi-circle = 1/2 πr²

→ 1/2 × 22/7 × (10)²

→ 2200/14

→ 157 cm² (approx.)

Add up all these values to find the area of cross-section

→ (180 + 500 + 157) cm²

→ 837 cm²