Question

Help!! Can someone explain this to me I’m not getting it.

Answer 1

Answer:

A. 99 sq cm

Step-by-step explanation:

Area of geometric shape

= 2 times the area of one triangle with base a and height c

+ 2 times the area of one triangle with base c and height b

+ Area of rectangle with dimensions a and c.

$= 2 \times \frac{1}{2} ac + 2 \times \frac{1}{2} bc + ac \\ \\ = ac + bc + ac \\ \\ = 2ac + bc \\ \\ = 2(13)(3) + 7(3) \\ \\ = 78 + 21 \\ \\ = 99 \: sq \: cm$

Answer 2

Answer: Choice A) 99 square cm.

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Explanation:

The rectangular base has area of length*width = a*c = 13*3 = 39 square cm. Let m = 39 since we'll use it later.

The triangles on the left and right sides have an area of base*height/2 = c*b/2 = 3*7/2 = 21/2 = 10.5 sq cm. They combine to an area of 2*10.5 = 21 sq cm. Let n = 21 since we'll use it later.

The triangles in the north and south positions have base 'a' and height 'c', so the area of each is base*height/2 = a*c/2 = 13*3/2 = 39/2 = 19.5 sq cm. That means the two north and south triangles add up to 19.5+19.5 = 39 sq cm. Let p = 39 since we'll use it later.

Overall, we have a total area of m+n+p = 39+21+39 = 99

The area of this flat 2D figure is 99 sq cm. If we folded along the dashed lines, then we'd get a 3D rectangular pyramid that has surface area of 99 sq cm. The surface area is the amount of material along the outside of the 3D figure. Or you can think of it like saying "If we painted all four sides of the 3D pyramid, then we cover 99 cm^2 of area".