Mathematics, 31.03.2020 21:40 matius0711

A composite figure is comprised of a square, trapezoid, and a rectangle. The square has side lengths of 10 centimeters. The trapezoid has base lengths of 8 centimeters and 14 centimeters. The height of the trapezoid is 4 centimeters. The rectangle has side lengths of 20 centimeters and 6 centimeters.

What is the area of the composite figure?

262 cm2
264 cm2
266 cm2
268 cm2

Answers: 1

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Answers

The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.

Step-by-step explanation:

The given is,

Dimensions of square has length of 10 cm

Trapezoid has base lengths of 8 cm and 14 cm

The length of the trapezoid is 4 cm

Rectangle has side length of 20 cm and 6 cm

Step:1

Area of composite figure = Area of square + Area of Trapezoid

+ Area of rectangle.......................(1)

Step:2

Formula for area of square,

$A_{square} = a^{2}$

where, a - side of length = 10 cm

$=10^{2}$

=100

Area of square, $A_{square}$ = 100 Square centimeter

Step:3

Formula for area of Trapezoid,

$A_{Trapezoid}$ = $\frac{a+b}{2} h$ .......................................(2)

Where, a - 8 cm

b - 14 cm

h - 4 cm

From equation (2)

= $\frac{8+14}{2} 4$

= (11)(4)

= 44

Area of Trapezoid, $A_{Trapezoid}$ = 44 square centimeters

Step:4

Formula for area of rectangle,

$A_{Rectangle} =lb$ ......................................(3)

Where, l = 20 cm

b = 6 cm

Equation (3) becomes,

= (20)(6)

= 120

Area of rectangle, $A_{Rectangle}$ = 120 square centimeters

Step:5

From Equation (1),

$A_{Composite}$ = 100 + 44 + 120

= 264 square centimeters

Result:

The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.

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