Question

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

Answer 1

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.

Answer 2

Answer: b)

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