Area and perimeter of pentagon are 675 cm² and
90 cm.
Area and perimeter of trapezoid are 119 cm² and 34 + 14√2 cm.
How to calculate the area and perimeter of shapes.
From the figure
For the Pentagon
It has five triangles with 18 cm and 15 cm.
Area of each triangle
Area = 1/2* b * h
= 1/2 * 18 * 15
= 9*15
= 135 cm²
Area of the Pentagon = 5 *:135
A = 675 cm²
Perimeter of pentagon = 5 * l
l = 18 cm
P = 18 * 5
= 90 cm
For the trapezoid
The slant height of the trapezoid is gotten from Pythagorean theorem
The base of the triangles of the trapezoid is
24 - 10 = 14
14/2 = 7 cm
L² = 7² + 7²
= 49 + 49
L² = 98
L = 7√2 cm
Area of trapezoid = 1/2(a + b)h
a = 10, b = 24, h = 7
Area = 1/2(10 + 24)7
= 17 * 7 = 119 cm²
Perimeter of trapezoid
P = 10 + 24 + 7√2 + 7√2
= 34 + 14√2 cm.