Question

Please help me with this question and provide an explanation. Thanks

Answer 1

36 cm²

Explanation:

this composite figure can be divided into a rectangle and the upper half will be considered as a triangle.

area of rectangle = l * w = 6 * 4 = 24 cm²

area of triangle = 1/2 * h * b

where base = 6

height = ?

according to Pythagoras theorem,

height, h will be equal to

h² = a² - b²

h² = 5² - 3² = 25 - 9 = 16

h = 4

thus, area of triangle = 1/2 * 4 * 6 = 12 cm²

area of figure = area of rectangle + area of triangle

= 24 + 12 = 36 cm²

Answer 2

Answer: 36 square cm

Explanation

Sub-divide the figure as shown below. I split the pentagon into:

• two right triangles up top
• a rectangle down below

Each right triangle is a 3-4-5 right triangle. Refer to the pythagorean theorem. The area of one of those right triangles is

area = 0.5*base*height = 0.5*3*4 = 6

Therefore, two cloned mirror copies gives an area of 2*6 = 12 square cm.

Then we add on the area of the rectangle (6*4 = 24) to get a total area of 12+24 = 36 square cm.