Question

What is the area of the figure below ?

Answer 1

58 in²

Explanation:

Separate the figure into 3 separate shapes:

• The triangle at the bottom
• The triangle at the top
• The trapezoid in the middle

The find the formulas you will use to solve each one:

• Trapezoid:
  `[h(b1 + b2)]0.5`

• Triangles:
  `0.5 (b * h)`

Plug in the values:

• Triangle at the top: (8 x 6)0.5 = 24 in²

• Trapezoid in the middle: [5(6 + 4)]0.5 = 25 in²
• Triangle at the bottom: (8 x 6)0.5 = 9 in²

Then add up all of the values:

• 24 + 25 + 9 = 58

Add the term:

• 58 in²

Answer 2

Explanation:

Area of the figure = area of the down triangle + area of trapezium + area of the upper triangle

Down triangle:

Base b = 8 in

Height = 6 in

`Area = (1)/(2)bh\\=(1)/(2)*8*6\\\\=4*6`

= 24 in²

Trapezium:

bases a = 4 in & b = 6 in

Height h = 5 in

`Area=((a+b)h)/(2)\\\\=((4+6)*5)/(2)\\\\=(10*5)/(2)\\\\=5*5`

= 25 in²

Area of the upper triangle:

Base b = 6 in

Height = (8 - 5) = 3 in

`Area=(1)/(2)bh\\\\=(1)/(2)*6*3\\\\=3*3`

= 9 in²

Area of the figure = 24 + 25 + 9 = 58 in²