Question

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Answer 1

QUESTION 1

The area of a triangle is given by

$Area=\frac{1}{2}\times base\times heigth$

The length of the base of the triangle is $6\:in.$ and the vertical height is $8\:in.$.

We substitute these values into the formula to obtain,

$Area=\frac{1}{2}\times 6\times 8$

$Area=3\times 8$

$Area=24\:in^2$

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 $7\:cm$

The area of a square is given by

$Area=l^2$

$\Rightarrow Area=7^2$

$\Rightarrow Area=49cm^2$.

The area of one of the triangles is

$Area=\frac{1}{2}\times base \times height$

The height of the triangle is $4cm$.

The base of the triangle is on one side of the square, so it is $7cm$.

The area now becomes

$Area=\frac{1}{2}\times 7 \times 4$

$\Rightarrow Area=7 \times 2$

$\Rightarrow Area=14cm^2$.

Since there are three identical triangles, we multiply the area of one triangle by 3 to get area of the three triangles.

$Area\:of\:the\:three\:triangles=3\times14=42cm^2$

The area of the logo is equal to the area of the square plus the area of the three identical triangles.

$Area\:of\:logo=49+42=91cm^2$

Hence the area of the logo is $91cm^2$

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

$Area=l\times w$

The width of the bigger rectangle is $5$ and the length is $25$.

$Area\:of\:bigger\: rectangle=25\times 5$

$Area\:of\:bigger\: rectangle=125\:square\:units$

The width of the smaller rectangle is $8$.

The length of the smaller rectangle is $25-(6+6)=25-12=13$.

$Area\:of\:smaller\: rectangle=13\times 8$

$Area\:of\:smaller\: rectangle=104\:square\:units$.

The two triangles are identical, so we find the area of one and multiply by 2

$Area\:of\:triangle=\frac{1}{2}\times base \times heigth$

$Area\:of\:triangle=\frac{1}{2}\times 6 \times 8$

$Area\:of\:triangle=3 \times 8$

$Area\:of\:triangle=24\:square\:units$

$\Rightarrow Area\:of\:the\:two\:triangles=2\times24=48\:square\:units$

The area of the figure is

$=125+104+48=277\:sqaure\:units$

The correct answer is C