Question

Find the area of the shaded region

Answer 1

Answer:

Area of the shades region = 244.6 ft²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle ABCD- Area of the right angle triangle DEC

Area of the rectangle = Length × width

                                    = 29.8 × 13

                                    = 387.4 ft²

By applying Pythagoras theorem in the right triangle DEC,

(Hypotenuse)² = (leg 1)² + (leg 2)²

CD² = DE² + EC²

(29.8)² = DE² + (28)²

888.04 = DE² + 784

DE² = 888.04 - 784

DE = 10.2 ft

Area of ΔDEC = $\frac{1}{2}(\text{Base})(\text{Height})$

                        = $\frac{1}{2}(10.2)(28)$

                        = 142.8 ft²

Area of the shades region = 387.4 - 142.8

                                             = 244.6 ft²