Question

Please help! Will give brainiest! (more than 5 points)

Answer 1

Answer:

A = (4.5π + 18) cm²

P = 3π + 6(1 + √2) cm

Step-by-step explanation:

Give figure is a composite structure of one semicircle and one right triangle.

Therefore, area of the figure = Area of the semicircle + Area of the triangle

Area of the given semicircle = $\frac{1}{2}(\pi r^{2} )$

Here r = radius of the semicircle

Area of the semicircle = $\frac{1}{2}(\pi )(3)^2$ [Given : AB = BC]

                                     = 4.5π cm²

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

                                 = $\frac{1}{2}(6)(6)$

                                 = 18 cm²

Total area = 4.5π + 18

             A = (4.5π + 18) cm²

Perimeter of the figure = Circumference of the semicircle + AB + AC

Circumference of the semicircle = πr

                                                      = 3π

AB = 6 cm

AC = $\sqrt{(\text{AB})^2+(\text{BC})^2}$

     = $\sqrt{6^2+6^2}$

     = $6\sqrt{2}$

Perimeter 'P' = 3π + 6 + $6\sqrt{2}$

                     = 3π + 6(1 + √2) cm