Question

The answer please! <3

Answer 1

Answer: b)
`100cm^2`

Explanation:

We have a triangle and a rectangle.

Let's solve each one separately.

Triangle:

a=5cm

b=? 12cm

c=13cm

To find b, use pythagorem's theorem.

`c^2=a^2+b^2`

Solve for b;

`b^2=c^2-a^2\\b=\sqrt[]{c^2-a^2}`

`b=\sqrt[]{(13)^2-(5)^2} \\b=\sqrt[]{169-25} \\b=\sqrt[]{144} \\b=12`

Find the area of this right triangle. The formula is:
`A=(1)/(2)ab`

`A=(1)/(2)(5cm)(12cm)\\ A=(1)/(2)(60)cm^2\\ A=30cm^2`

Now let's solve the rectangle;

Rectangle:

Length: 14cm (because we found that the base of the triangle was 12, plus 2cm which are next to the height of 5cm, you add them up and you get 14. Or, you can see that the lower base of the rectangle must be equal to the upper base, therefore you can conclude it's 14 cm.

Width: 5cm

The formula for the area of a rectangle is simply multiply 2 of its sides.

`A=w*l\\A=(5cm)(14cm)\\A=70cm^2`

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After having found both areas, add them together.

30 + 70 = 100
`cm^2`

This is the area of the composite figure.