Question

find the area of given figure​

Answer 1

Answer:

Total area of figure=188cm²

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Explanation:

We can see that the given figure is made up of a right angled triangle, a square and a trapezium. We can find the area of whole figure by finding area of each and adding them.

So let's start!!

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Given:

• Height of triangle=10cm

• Base of triangle=8cm

• Side of square=8cm

• Opposite || sides of trapezium=8cm and 20cm.

• Height of whole figure=24cm

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To find:

• Areas of figure

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Solution:

The height of trapezium is not given in the figure so let's find it first!

⇒ Height of whole figure=Height of (∆+Square+Trapezium)

⇒ 24cm=(10cm)+(8cm)+(height of trapezium)

⇒ 24cm-10cm-8cm= Height of trapezium

⇒ 6cm= Height of trapezium

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~Now finding area of trapezium

Area of trapezium=½×(Sum of || sides)× height

Area of trapezium=½×(20cm+8cm)×6cm

Area of trapezium=½×(28cm)×6cm

Area of trapezium=14cm×6cm

Area of trapezium=84cm²

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~Now finding area of square

Area of square=Side²

Area of square=(8cm)²

Area of square=(8cm)×(8cm)

Area of square=64cm²

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~Now finding area of triangle

Area of right angled ∆=½×Base×Height

Area of right angled ∆=½×(8cm)×(10cm)

Area of right angled ∆=4cm×(10cm)

Area of right angled ∆=40cm²

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~Now finding total area

Total area of figure=Area of (∆+Square+Trapezium)

Total area of figure=(40cm²)+(64cm²)+(84cm²)

Total area of figure=40cm²+64cm²+84cm²

Total area of figure=(104cm²)+(84cm²)

Total area of figure=188cm²

So the required total area of figure=188cm²

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Answer 2

Answer:

188 cm ^2 is the area of the given figure.

Step-by-step explanation:

Firstly naming the polynomial (attachment attached)

To find :

• the area of the given figure =

       Area of Δ ABC + Area of square BCDE + Area of trapezium DEFG

Given :

→ In Δ ABC

• AB = 10 cm
• BC = 8 cm

→ In square BCDE

• BC = CE = DE = BD = 8 cm [ ALL SIDES ARE EQUAL OF A SQUARE ]

→ In trapezium DEFG

• GF = 20 cm
• DE = 8 cm (Side of a square)

Formula to be used :

• Area of triangle = $\frac{1}{2}$ X base X height
• Area of Square =  Side X Side
• Area of trapezium = $\frac{1}{2}$ X sum of parallel sides X height
• Area of Δ ABC + Area of square BCDE + Area of trapezium DEFG = Area of the given figure
• Formula for hypotenuse = a² + b² = $c^2$ [ a = side of right triangle, b = side of right triangle, c = hypotenuse ]

[Note : hypotenuse isn't required for finding area of a triangle you can find it for extra information]

Area of Δ ABC :

= $\frac{1}{2}$ X base X height

= $\frac{1}{2}$ X 8 X 10

= 40 cm^2

Area of Square BCDE:

= Side X Side

= 8 X 8

= 64 cm ^2

Area of trapezium DEFG :

Height = height of the figure ( 24 cm ) - AD ( 10 + 8 = 18)

=24 cm - 18 cm = 6 cm

= $\frac{1}{2}$ X sum of parallel sides X height

= $\frac{1}{2}$ X (20 + 8 ) X 6 cm

= $\frac{1}{2}$ X 28 X 6 cm

= $\frac{168}{2}$

= 84 cm ^2

Area of the given figure :

= Area of Δ ABC + Area of square BCDE + Area of trapezium DEFG

= 40 +64 + 84

= 188 cm ^2

188 cm ^2 is the area of the given figure.