1 Answer

Marcos R · Answer 1 · 2023-08-27T15:48:55+0000

To solve this question, we need to calculate the area of each face of the composite figure and sum them all.

Let's analyze the faces of the figure:

· 2 triangles of base 12cm and height 5cm

· 1 rectangle of base 13cm and height 4cm (in the blue part)

· 1 rectangle of base 5cm and height 5cm (also in the blue part)

· 2 rectangles of base 12cm and height 3cm

· 2 rectangles of base 4cm and height 3cm

·1 rectangle of base 12cm and height 4cm

Now, we need to calculate the areas of those figures. The formula for the area of a triangle is:

$A_(traingle)=(base\cdot height)/(2)$

The formula for the area of a rectangle is:

$A_(rectangle)=base\cdot height$

Now we use the formulas and the lengths listed above to find each area:

· 2 triangles of base 12cm and height 5cm:

$A_1=(12\cdot5)/(2)=30cm^2$

· 1 rectangle of base 13cm and height 4cm (in the blue part):

$A_2=13\cdot4=52cm^2$

· 1 rectangle of base 4cm and height 5cm (also in the blue part)

$A_3=4\cdot5=20cm^2$

· 2 rectangles of base 12cm and height 3cm:

$A_4=12\cdot3=36cm^2$

· 2 rectangles of base 4cm and height 3cm:

$A_5=4\cdot3=12cm^2$

·1 rectangle of base 12cm and height 4cm:

$A_6=12\cdot4=48cm$

Now, we add all the areas, but we need to remember to multiply by 2 the repeated faces. The total surface area of the figure is:

$A=2\cdot30+52+20+2\cdot36+2\cdot12+48=60+52+20+72+24+48=276cm^2$

Thus, the answer is:

Please log in or register to add a comment.