QUESTION 1
The area of a triangle is given by
[tex]Area=\frac{1}{2}\times base\times heigth[/tex]
The length of the base of the triangle is [tex]6\:in.[/tex] and the vertical height is [tex]8\:in.[/tex].
We substitute these values into the formula to obtain,
[tex]Area=\frac{1}{2}\times 6\times 8[/tex]
[tex]Area=3\times 8[/tex]
[tex]Area=24\:in^2[/tex]
The area of the triangle is 24 square inches.
The correct answer is A
QUESTION 2
The company logo is made up of three triangles and a square.
The length of the square is [tex]7\:cm[/tex]
The area of a square is given by
[tex]Area=l^2[/tex]
[tex]\Rightarrow Area=7^2[/tex]
[tex]\Rightarrow Area=49cm^2[/tex].
The area of one of the triangles is
[tex]Area=\frac{1}{2}\times base \times height[/tex]
The height of the triangle is [tex]4cm[/tex].
The base of the triangle is on one side of the square, so it is [tex]7cm[/tex].
The area now becomes
[tex]Area=\frac{1}{2}\times 7 \times 4[/tex]
[tex]\Rightarrow Area=7 \times 2[/tex]
[tex]\Rightarrow Area=14cm^2[/tex].
Since there are three identical triangles, we multiply the area of one triangle by 3 to get area of the three triangles.
[tex]Area\:of\:the\:three\:triangles=3\times14=42cm^2[/tex]
The area of the logo is equal to the area of the square plus the area of the three identical triangles.
[tex]Area\:of\:logo=49+42=91cm^2[/tex]
Hence the area of the logo is [tex]91cm^2[/tex]
QUESTION 3
Since the figure is made up of two rectangles and two right triangles, we find their areas and sum them to get the area of the figure.
The area of a rectangle is given by
[tex]Area=l\times w[/tex]
The width of the bigger rectangle is [tex]5[/tex] and the length is [tex]25[/tex].
[tex]Area\:of\:bigger\: rectangle=25\times 5[/tex]
[tex]Area\:of\:bigger\: rectangle=125\:square\:units[/tex]
The width of the smaller rectangle is [tex]8[/tex].
The length of the smaller rectangle is [tex]25-(6+6)=25-12=13[/tex].
[tex]Area\:of\:smaller\: rectangle=13\times 8[/tex]
[tex]Area\:of\:smaller\: rectangle=104\:square\:units[/tex].
The two triangles are identical, so we find the area of one and multiply by 2
[tex]Area\:of\:triangle=\frac{1}{2}\times base \times heigth[/tex]
[tex]Area\:of\:triangle=\frac{1}{2}\times 6 \times 8[/tex]
[tex]Area\:of\:triangle=3 \times 8[/tex]
[tex]Area\:of\:triangle=24\:square\:units[/tex]
[tex]\Rightarrow Area\:of\:the\:two\:triangles=2\times24=48\:square\:units[/tex]
The area of the figure is
[tex]=125+104+48=277\:sqaure\:units[/tex]
The correct answer is C
