Question

What is the area of the shaded region?

Answer 1

Area of Composite Shapes

To find the area of composite shapes, we can break the bigger shape down into small, simpler shapes, and find the sum of their areas.

For this triangle, we will need to know the formula to find the area of a triangle:

$A=\dfrac{1}{2}bh$

Solving the Question

The given shape can be seen as one large triangle with a little triangle cut out of it. To find the shaded region, we can:

1. Find the area of the large triangle
2. Find the area of the little triangle
3. Subtract the area of the little triangle from the large triangle

Area of the Large Triangle

$A=\dfrac{1}{2}bh$

⇒ Plug in the values given for the base and height:

$A=\dfrac{1}{2}(5)(2+4+6)\\\\A=\dfrac{1}{2}(5)(12)\\\\A=(5)(6)\\\\A=30 mm^2$

Area of the Small Triangle

$A=\dfrac{1}{2}bh$

⇒ Plug in the values given for the base and height:

$A=\dfrac{1}{2}(3)(4)\\\\A=(3)(2)\\\\A=6mm^2$

Subtract the Area of the Small Triangle from the Area of the Large Triangle

$30 mm^2-6mm^2\\=24mm^2$

Answer

The area of the shaded region is $24mm^2$.