In parallelogram ABCD, points E and F are the midpoints of side AB and BC, respectively. A F meets DE at G and BD at H. What is the area of quadrilateral BHGE if the area of ABCD is 60?

The area of the quadrilateral B-H-G-E is 7

Step-by-step explanation:

The area of the parallelogram = 60  

It can be shown that ΔG-D-F = 3/10 × Area of the parallelogram S = 3/10×S

Because the diagonal B-D shares A-F into the ratio 1:2, the ΔH-D-A = 2/3×ΔD-B_A  where ΔD-B_A = 1/2·S, therefore, ΔD-B_A = 2/3×1/2×S = 1/3×S

ΔB-F-H is similar to ΔD-B_A scaled to 1/2,

Therefore;

The area of ΔB-F-H = 1/4×Area of ΔD-B_A = 1/4×1/3×S = 1/12×S,

ΔF-C-D = 1/4×S

ΔE-A-D = 1/4×S

The area of the quadrilateral B_H_G_E found as follows;

Area B_H_G_E  = S - (ΔF-C-D + ΔG-D-F +ΔE-A-D +ΔB-F-H)

Area B_H_G_E  = S - (1/4×S + 1/10×S +1/4×S +1/12×S) = S - 53/60×S = 7/60×S

Whereby we are given that the area, S of the parallelogram AB-CD = 60 we have;

Area B_H G_E  = 7/60×60 = 7

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

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step-by-step explanation: