Question

Find areas of the trapezoids.
(I'm giving 100 points to whoever answers.)

Answer 1

a) Area of STAR = 48 square units

b) Area of SKCO = 42 square units

Explanation:

The formula for the area of a trapezoid is half the sum of the bases multiplied by the height:

`\boxed{\sf Area=(a+b)/(2) \cdot h}`

The bases of a trapezoid are the parallel sides.

The height of a trapezoid is the perpendicular distance between the two bases.

a) Trapezoid STAR

The bases are parallel sides SR and TA.

The height is the perpendicular distance between SR and TA.

Therefore:

• a = SR = 4 units
• b = TA = 8 units
• h = 8 units

Substitute these values into the formula and solve for area:

`\begin{aligned}\sf \implies Area\;STAR&=(4+8)/(2) \cdot 8\\\\&=(12)/(2) \cdot 8\\\\&=6\cdot 8\\\\&=48\;\sf square\;units\end{aligned}`

b) Trapezoid SKCO

The bases are parallel sides SK and OC.

The height is the perpendicular distance between SK and OC.

Therefore:

• a = SK = 4 units
• b = OC = 10 units
• h = 6 units

Substitute these values into the formula and solve for area:

`\begin{aligned}\sf \implies Area\;SKCO&=(4+10)/(2) \cdot 6\\\\&=(14)/(2) \cdot 6\\\\&=7 \cdot 6\\\\&=42\;\sf square\;units\end{aligned}`