Question
A hand fan is made by sticking 10 equal size triangular strips of two different types of paper as shown in the figure. The dimensions of equal strips are 25cm, 25cm and 14cm. Find the area of each type of paper needed to make the hand fan.
✓
Answer
Given that, $A O=25 cm O B=25 cm B A=14 cm$
Area of each strip $=$ Area of $\triangle AOB$
Now, for the area of $\triangle AOB$
$\text { Perimeter }=A O+O B+B A 2 s=25 cm+25 cm+14 cm s=32 cm$
By using Heron's Formula, Area of the
$\triangle AOB=\sqrt{s \times(s-a) \times(s-b) \times(s-c)}$
$=\sqrt{32 \times(7) \times(4) \times(18)}$
$=168 cm^2$
Also, area of each type of paper needed to make a fan $=5 \times$ Area of $\triangle AOB$
Area of each type of paper needed to make a fan $=5 \times 168 cm^2$
Area of each type of paper needed to make a fan $=840 cm^2$.
Area of each strip $=$ Area of $\triangle AOB$
Now, for the area of $\triangle AOB$
$\text { Perimeter }=A O+O B+B A 2 s=25 cm+25 cm+14 cm s=32 cm$
By using Heron's Formula, Area of the
$\triangle AOB=\sqrt{s \times(s-a) \times(s-b) \times(s-c)}$
$=\sqrt{32 \times(7) \times(4) \times(18)}$
$=168 cm^2$
Also, area of each type of paper needed to make a fan $=5 \times$ Area of $\triangle AOB$
Area of each type of paper needed to make a fan $=5 \times 168 cm^2$
Area of each type of paper needed to make a fan $=840 cm^2$.
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