Mathematics: The area of a triangle reduced by the area of the semicircle is ( 48 - 2π ) square meters. The base of the triangle is 12 meters. Find the height of the triangle and radius of the semicircle.

Step-by-step explanation:ijH89hE6DTD7dtc7it6u8...

The area of a triangle reduced by the area of - id9220361, haileesprague3999

angelteddy033

10.02.2022

The height of the triangle is 8 meters and the radius of the semi-circle is 2 meters

Step-by-step explanation:

The area of a triangle = $\frac{1}{2}$ × b × h, where

b is the length of the baseh is the length of the height

The area of a semi-circle = $\frac{1}{2}$ π r², where

r is the length of the radius

∵ The area of the figure = Area Δ - Area semicircle

∵ The area of the figure = $\frac{1}{2}$ × b × h - $\frac{1}{2}$ π r²

∵ The base of the triangle is 12 meters

→ Substitute it in the area of the figure above

∴ The area of the figure = $\frac{1}{2}$ × 12 × h - $\frac{1}{2}$ π r²

∴ The area of the figure = 6h - $\frac{1}{2}$ π r²

∵ The area of the figure = 48 - 2 π

→ Equate the two expressions of the area of the figure

∴ 6h - $\frac{1}{2}$ π r² = 48 - 2 π

→ Equate the like terms of the two sides

∵ 6h = 48

→ Divide both sides by 6 to find h

∴ h = 8

∵ - $\frac{1}{2}$ π r² = -2 π

→ Divide both sides by -π

∴ $\frac{1}{2}$ r² = 2

→ Multiply both sides by 2

∴ r² = 4

→ Take √ for both sides

∴ r = 2

The height of the triangle is 8 meters and the radius of the semi-circle is 2 meters

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