Question

6. Find the area of the given regular octagon having each side equal to 5 cm. HC =11 cm and AL = 4 cm. B. 4 cm С H L 11 cm D G E F​

Answer 1

Answer:

AP=4 cm

All sides =5 cm

HC=GD=11 cm

Area of trapezium ABCH

=Area of trapezium GDEF

Area of a trapezium =

2

1

(a+b)h

$$=\dfrac{1}{2}(5+11)\times 4$

=32 cm

2

So Area of trapezium GDEF=32 cm

2

Area of rectangle MCDG=l×b=11×5=58 cm

2

Area of Octagon = Area of two trapezium + Area of rectangle

22×32+55

=64+55=119 cm

2

Answer 2

Step by step Explanation:

Given: Regular octagon having each side equal to 5 cm. HC =11 cm and AL = 4 cm.

To find: Area of regular octagon.

Solution:

Tip:

1)Area of trapezium $\bf=\frac{1}{2}\times \text{perpendicular height}(\text{sum of parallel sides})$

2) Area of rectangle$\bf =length\times breadth$

Step 1: Write the divisions of octagon.

Area of trapezium HABC+Area of trapezium GDEF+ Area of rectangle HGDC

Step 2: Find the area of trapezium HABC.

Parallel sides are HC=11 cm and AB =5 cm

Perpendicular height = 4 cm

Area of trapezium HABC $=\frac{1}{2}\times 4(11+5)$

$=\frac{1}{2}\times 4(16)$

Area of trapezium HABC$=32\:cm^2$

Step 3: Find area of trapezium GDEF

All dimensions are same.

So,

Area of trapezium GDEF$=32\:cm^2$

Step 4: Find area of rectangle HGDC.

Length = 11 cm

Breadth = 5 cm

Area of HGDC=55 cm²

Step 5: Calculate area of octagon.

Add the results of step 2- step 4

=32+32+55

=119 cm²

Final answer:

Area of regular octagon is 119 cm²

Hope it will help you.

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