Question

10.) find the area of a trapezoid with base lengths of 12in. and 18in. and a height of 7 in.
11.) find the area of a rhombus with diagonal lengths 12in. and 19in.
12.) if the area of a rhombus is 60 squared inches and a diagonal measures 8 in. what is the measure of the other diagonal?
13.) if a trapezoid has an area of 144 squared inches and the bases are 7 in. and 10 in., what is the height?
14.) if a kite has an area of 240 squared inches and one diagonal that measures 17 in., what is the measure of the other diagonal?
15.) if a kite has two diagonals that measure 15 in. and 24 in., what is the area of the kite?

Explanation:

Question 10

Step1: Recall trapezoid area formula

The formula for the area of a trapezoid is \( A=\frac{(b_1 + b_2)h}{2} \), where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.

Step2: Substitute the given values

Here, \( b_1 = 12 \) in, \( b_2=18 \) in, and \( h = 7 \) in. Substitute these values into the formula:
\( A=\frac{(12 + 18)\times7}{2} \)

Step3: Simplify the expression

First, add the bases: \( 12+18 = 30 \). Then multiply by the height: \( 30\times7=210 \). Then divide by 2: \( \frac{210}{2}=105 \).

Step1: Recall rhombus area formula

The formula for the area of a rhombus is \( A=\frac{d_1\times d_2}{2} \), where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

Step2: Substitute the given values

Here, \( d_1 = 12 \) in and \( d_2 = 19 \) in. Substitute into the formula:
\( A=\frac{12\times19}{2} \)

Step3: Simplify the expression

First, multiply the diagonals: \( 12\times19 = 228 \). Then divide by 2: \( \frac{228}{2}=114 \).

Step1: Recall rhombus area formula

The formula for the area of a rhombus is \( A=\frac{d_1\times d_2}{2} \), where \( A \) is the area, \( d_1 \) and \( d_2 \) are the diagonals. We know \( A = 60 \) square inches and \( d_1=8 \) in. We need to find \( d_2 \).

Step2: Rearrange the formula to solve for \( d_2 \)

From \( A=\frac{d_1\times d_2}{2} \), we can multiply both sides by 2: \( 2A=d_1\times d_2 \), then divide both sides by \( d_1 \): \( d_2=\frac{2A}{d_1} \)

Step3: Substitute the given values

Substitute \( A = 60 \) and \( d_1 = 8 \) into the formula: \( d_2=\frac{2\times60}{8} \)

Step4: Simplify the expression

First, multiply 2 and 60: \( 2\times60 = 120 \). Then divide by 8: \( \frac{120}{8}=15 \)

Answer:

The area of the trapezoid is \( 105 \) square inches.

Question 11