Question

Can someone please explain this to me

Answer 1

A = 15 units²

Explanation:

the area (A) of the shaded triangle is calculated as

A = area of rectangle enclosing the triangle - area of white triangles on either side of shaded triangle and the one on top

area of rectangle = 10 × 5 = 50 units²

area of 2 congruent triangles = 2 ×
`(1)/(2)` × 5 × 5 = 5 × 5 = 25 units²

area of top triangle =
`(1)/(2)` × 10 × 2 = 5× 2 = 10 units²

A = 50 - 25 - 10= 15 units²

Answer 2

`15u^(2)`

Explanation:

let's say each square is =
`1u^(2)`

triangle A area: 2*5

`(2*5)/(2)=5u^(2)`

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triangle B area: 2*2

`(2*2)/(2)=2u^(2) \\Triangle A - B = 5 - 2= 3u^(2)`

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next figure

triangle C area 3*3

`(3/3)/(2)=4.5u^(2)\\ -------------\\\\3u^(2)+4.5u^(2)=7.5u^(2)\\ -------------\\`

And since the other figure is a reflection *2

`7.5u^(2)*2=15u^(2)`