Question

9. What formula could be used to find the area of the image?

Answer 1

Answer:

9. Area of triangle= $\frac{1}{2} \times base\times height$

10. Base= 16 ft and Height= 15 ft.

11. 120 ft²

Step-by-step explanation:

Given: Base of triangle= 16 ft

           Length of leg of triangle= 17 ft.

As shown in the picture that median has bisected the triangle and forming two right angle triangle.

∴ Each base of right angle triangle= $\frac{16}{2} = 8\ feet$

Now, finding the height of triangle by using pythagorean theorem.

We know, $h^{2} = a^{2} +b^{2}$, where h is hypotenous, a is height or opposite and b is base or adjacent of triangle.

⇒ $17^{2}= a^{2} + 8^{2}$

⇒$289= a^{2} + 64$

Subtracting both side by 64

⇒ $225= a^{2}$

taking square root on both side, remember; √a²=a

⇒a= $\sqrt{225} = 15$

Hence, height of triangle is 15 ft.

Next, finding the area of triangle.

Formula; Area of triangle= $\frac{1}{2} \times base\times height$

⇒ Area of triangle= $\frac{1}{2} \times 16\times 15$

∴ Area of triangle= 120 ft²