Find the area of each shape by decomposing each shape into rectangle and/or triangle. for #1, i got 52, is this correct? for #2, i got 120, is this correct?

Remark

You don't have to decompose the second one, and it is better if you don't. Just find the area as you probably did: use the formula for a trapezoid. You have to assume that the 6cm line hits the 2 bases at right angles for each of them, otherwise, you don't know the height. So I'm going to assume that we are in agreement about the second one.

Problem One

The answer for this one has to be broken down and unfortunately, you answer is not right for the total area, although you might get 52 for the triangle. Let's check that out.

Triangle

Area = 1/2 * b * h

base = 16 cm

h = 10 - 4 = 6

Area = 1/2 * 16 * 6

Area = 48

Area of the Rectangle

Area = L * W

L = 16

W = 4

Area = L * W

Area = 16 * 4

Area = 64

Total Area

Area = 64 + 48

Area = 112  of both figures <<<< Answer

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

both equations and proportions are better.