Question

What is the area in square units of triangle QRS also show work

Answer 1

The correct option is : A. 7

Explanation:

According to the below diagram, for rectangle AQBC, the length
`=5` units and the width
`= 4` units.

So, the area of the rectangle
`= (length* width)= (5* 4)= 20` square units.

For
`\triangle AQS,` base
`(AS)= 3` units and height
`(AQ)= 4` units.

So, area of
`\triangle AQS`
`=(1)/(2)* base * height =(1)/(2)(3)(4)=6` square units.

For
`\triangle CSR,` base
`(CR)= 2` units and height
`(CS)= 2` units.

So, area of
`\triangle CSR`
`=(1)/(2)* base * height =(1)/(2)(2)(2)=2` square units.

For
`\triangle BQR,` base
`(BR)= 2` units and height
`(BQ)= 5` units.

So, area of
`\triangle BQR`
`=(1)/(2)* base * height =(1)/(2)(2)(5)=5` square units.

Now, total area of
`\triangle AQS`,
`\triangle CSR` and
`\triangle BQR`
`=(6+2+5)= 13` square units.

Thus, the area of
`\triangle QRS` =(Area of rectangle AQBC)-(Area of
`\triangle AQS`,
`\triangle CSR` and
`\triangle BQR`)
`=(20-13)= 7` square units.

Answer 2

Find the area of the larger rectangle.
5 x 4 = 20
One of the triangles is 2 x 2. Area of 2. Subtract 2 from 20.
20 - 2 = 18
Another is 2 x 5. Area of 5. Subtract 5 from 18.
18 - 5 = 13
The last is 3 x 4. Area of 6. Subtract 6 from 13.
13 - 6 = 7
The area of the triangle QRS is A, 7.
Hope this helps!