Find the perimeter and surface area

Question

https://ibb.co/Jj8jM5gX

Answer 1

Let's start with the trickiest piece first and calculate the perimeter.

Calculation of the perimeter:

1 - Calculation of the two top sides of the triangle is the most complicated part in this question. Assuming it is an isosceles triangle (given its visual regularity), the height drawn from the tip to the base of the triangle will divide the base into two equal parts. The height also splits the triangle into two identical right triangles. So we use Pythagoras theorem to calculate each missing side of the isosceles triangle.

hypotenuse (h) = ?

opposite (o) = 4

adjacent (a) = 4/2 = 2

h x h = (o x o) + (a x a) = 16 + 4 = 20

h = sqrt(20) = 4.47

2 - The perimeter (P) can now be calculated as follows (calculation is listed starting from the triangle moving clockwise around the shape):

P = (2 x 4.47) + 12 + 6 + 4 + 5 + 4 + 6 + 5 +6 + 4 + 6 +12

P = 78.94 m (note the unit i given in m and is included as part of the result!)

Calculation of the area:

This is the easier part of the problem. Let's first calculate the area of each component and add them up at the end:

1 - Area of triangle (S1): 1/2 x 4 x 4 = 8 m^2 (don't forget the unit is m)

2 - Area of rectangle below the triangle (S2): 4 x 12 = 48 m^2

3 - Area of rectangle at the bottom (S3): 6 x 15 = 90 m^2

4 - Area of the rectangle on the right (S4): 5 x 4 = 20 m^2

Let's calculate the total area (S) to finish:

S = S1 + S2 + S 3 + S4 = 8 + 48 + 90 + 20 = 166 m^2 (don't forget to include the unit with the answer!)

Answer 2

Let's call the parts, small triangle, small ,l medium, and large rectangles.

Triangle: has dimensions of 4 base, 4 height (isosceles, so sides are sqrt(2^2+4^2) = 2sqrt(5))

Perimeter = 2(2sqrt(5) Area = 1/2(4*4) = 8

Small rectangle: Perimeter = 2*4+5 Area = 4*5

Medium Rectangle Perimeter = 2*12 Area = 4*12

Large Rectangle Perimeter = 2*(6+15) - (5+4) Area = 6*15

Hope that helps. Please consider a tutor!