Question

Radha made a picture ofan aeroplane with coloured paper as shown in Fig 12.15. Find the total area of the paper used.

Answer 1

Dear Student,

Answer:
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White paper used = 6.5 sq-cm

Blue paper used= 2.5+6.5+1.29
= 10.29 sq-cm

Solution:
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Region I:
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Isosceles Triangle (two equal side a = 5, base b = 1)

Area of Isosceles Triangle =
$\frac{1}{2} \times b \times h$
$h = \sqrt{ {a}^{2} - \frac{ {b}^{2} }{4} } \\ \\ h = \sqrt{25 - \frac{1}{4} } \\ \\ h = \frac{99}{4} \\ \\ h = 4.97$
or h ≈ 5 cm

Area of region 1 =
$\frac{1}{2} \times 1 \times 5 \\ \\ = 2.5 \: \: {cm}^{2}$

2) Area of Region V,IV :
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Both have same dimensions ,these are right angle triangle

Base =1.5 cm

Height= 6 cm

Area =
$\frac{1}{2} \times b \times h \\ \\ = \frac{1}{2} \times 1.5 \times 6 \\ \\ = 4.5 \: \: {cm}^{2}$
Total area of both region V,IV = 2(4.5) = 9 sq-cm

3) Area of Region II:
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III region is a rectangle: length = 6.5 cm

breadth = 1 cm

Area of rectangle=
$l \times b \\ = 6.5 \times 1 \\ \\ = 6.5 {cm}^{2}$

Area of third region = 6.5 sq-cm

4) Area of Region III:
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III region is a trapezium

Area of trapezium= 1/2(sum of parallel sides)*h

= 1/2(3)(.86)

= 1.29 sq-cm

Hope it helps you.

Answer 2

Part I: - Isosceles triangle:

Sides are a = b = 5 cm, c = 1 cm.

We know that s = (a + b + c)/2

                           = (5 + 5 + 1)/2

                           = 11/2

                           = 5.5 cm.

We know that by heron's formula:

⇒ √s(s - a)(s - b)(s - c)

⇒ √(5.5)(5.5 - 5)(5.5 - 5)(5.5 - 1)

⇒ √(5.5)(0.5)(0.5)*(4.5)

⇒ √6.1875

⇒ 2.5 m².

Part II: - Rectangle:

Length of the Sides are 6.5 cm and 1 cm.

We know that Area of rectangle = length * breadth

⇒ 6.5 * 1

⇒ 6.5 cm².

Part III: - Trapezium:

Length of non-parallel sides are 1 cm and 2 cm.

⇒ Area of equilateral triangle + Area of trapezium

⇒ √3/4 a^2 + Base * Height

⇒ √3/4 (1)^2 + 1 * √3/2

⇒ 3√3/4

⇒ 1.3 cm².

Part - IV: - triangles:

Sides are 6 cm and height is 1.5 cm.

Area = (1/2) * base * height

        = (1/2) * 6 * (1.5)

        = 4.5 cm².

Area of IV and V are 4.5 cm² and 4.5 cm².

⇒ Area of the paper used = 2.5 + 6.5 + 1.3 + 4.5 + 4.5

⇒ 19.3 cm².

Therefore, total area of the paper used = 19.3 cm².

Hope this helps!