The area of the hexagon, if AB = BC = CD = DE = EF = FA = 13cm and AO = PD = 5cm

Question

The area of the hexagon, if AB = BC = CD = DE = EF = FA = 13cm and AO = PD = 5cm, is ___ $c m^{2}$

Options:

Answer: Option A
:

In the given figure, ∆AOB is right-angled triangle right angled at O.
So,

$\Rightarrow$ $A O^{2}$ + $O B^{2}$ = $A B^{2}$ .

$\Rightarrow$ $5^{2}$ + $O B^{2}$ = $13^{2}$ .

$\Rightarrow$ $O B^{2}$ = 169 - 25 = 144

$\Rightarrow$ OB = 12cm

So now the total area of the hexagon = 4 $\times$ Area of ∆AOB+ 2 $\times$ Area of rectangle BCPO

$\Rightarrow$ Area = 4 $\times$ ( $\frac{1}{2}$ $\times$ OB $\times$ AO) + 2 $\times$ (BC $\times$ OB)

$\Rightarrow$ Area = 4 $\times$ ( $\frac{1}{2}$ $\times$ 12 $\times$ 5) + 2 $\times$ (13 $\times$ 12)

$\Rightarrow$ Area = 4 $\times$ (30) + 2 $\times$ (156)

$\Rightarrow$ Area = 432 $c m^{2}$ .

Was this answer helpful ?

Next Question

More Questions on This Topic :

Question 1. The area of the floor of a rectangular hall of length 60 m is 1200 m2. The dimensions of the carpet available is ....m .Hence 25 such carpets are required to cover the hall.

Question 2. Abhishek has three containers: a)Cylindrical container A having radius r and height 2r b)Cubical container B having ....the containers in the increasing order of their volumes is

Question 3. If the height of a cylinder becomes one-eighth of the original height and the radius is doubled, then which of th....is doubled, then which of the following will be true?

Question 4. The surface areas of six faces of a cuboid are 12, 12, 36, 36, 48, 48, (all in cm2). The volume of the solid in cm3, i....cm2). The volume of the solid in cm3, is ____.

Question 5. How many small cuboids with dimensions 20 cm × 25 cm × 40 cm each can be accommodated in a cubical....be accommodated in a cubical box of edge 2 m ?

Question 6. A trapezium has an area of 570 cm2. The height of the trapezium is 5 cm and the larger parallel side is twice in lengt....in length as the smaller parallel side.Choose the correct option.

Question 7. The sides of a rectangle are in the ratio of 6 : 5 and its area is 750 sq.m. Find the perimeter of rectangle (in m). ....is 750 sq.m. Find the perimeter of rectangle (in m).

Question 8. A mat in the shape of a parallelogram has a height of 4 cm and a base of 3 cm. How much would it cost to cover a paral....of 180 sq. cm with mats, if each mat costs Rs.7?

Question 9. The perimeter of the given figure is ___ ....

Question 10. PQRS is a quadrilateral in which PQ=5√2cm, QR=5√2cm, RS=8cm, SP=6cm, ∠PSR=∠PQR=90∘. Then its area is....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

CBT Mixed Test 1 GPOE/GPA SAIL E0 2024

CBT Mixed Test 1 Reasoning SAIL E0 2024

GPOE / GPA Combined 1 Free CBT Mock Test SAIL E0 2024

Tabulation - Test Paper 5 Data Interpretation Reasoning & DI

Tabulation - Test Paper 4 Data Interpretation Reasoning & DI