Question

Complete the steps to find the area of the trapezoid.

Area of rectangle = _ square units

Area of triangle 1 = square units

Area of triangle 2 = _ square units

Area of triangle 3 = _ square units

Area of trapezoid = _ square units

Answer 1

Area of rectangle =256 square units

Area of triangle 1 = 24 square units

Area of triangle 2 = 16 square units

Area of triangle 3 = 96 square units

Area of trapezoid = 120 square units

Explanation:

Answer 2

Given:

In the given diagram

Each small box along X axis = 2 unit

Each small Box along Y axis = 2 unit

For rectangle:

Length = 16 unit

Width = 16 unit

For triangle 1

Base = 8 unit

Height = 6 unit

For triangle 2

Base = 8 unit

Height = 4 unit

For triangle 3

Base = 16 unit

Height = 12 unit

Formula

Area of the trapezoid is

`A = R -T_(1) -T_(2) -T_(3)`

Where,
`A` be the area of the trapezoid

`R` be the area of the rectangle

`T_(1) ,T_(2) ,T_(3)` be the area of the triangle 1, 2 and 3 respectively.

`R = lb` where, l be length and b the width

`T_(1) = (1)/(2) bh`, where, b be the base and h be the height

Now,

Taking, l = 16 and b = 16 we get,

`R = (16)(16)` = 256 sq unit

For Triangle 1

Taking, b = 8 and h = 6 we get,

`T_(1) = (1)/(2)(8)(6)` sq unit

`T_(1) = 24` sq unit

For Triangle 2

Taking, b = 8 and h = 4 we get,

`T_(2) = (1)/(2)(8)(4)` sq unit

`T_(2) = 16` sq unit

For Triangle 3

Taking, b = 16 and h = 12 we get,

`T_(3) = (1)/(2)(16)(12)` sq unit

`T_(3) = 96` sq unit

Therefore,

The area of the trapezoid is = 256-24-16-96 sq unit = 120 sq unit

Hence,

Area of rectangle =256 square units

Area of triangle 1 = 24 square units

Area of triangle 2 = 16 square units

Area of triangle 3 = 96 square units

Area of trapezoid = 120 square units